My affiliation is thereInstitute for Mathematics and Statisticsfrom the University of Helsinki (see also myDepartment home page).
Recently supported research projects:
- "Spectral Analysis of Limit Value Problems in Mathematical Physics" (Academy of Finland 2012),
- "Functional Analysis and Applications" (Academy of Finland 2010-2013),
- "Mathematical Models of Piezoelectric and Elastic Systems" (Academy of Finland 2013-2014)
- "Spectrum of Piezoelectricity System" (Academy of Finland 2015-2016)
- "Spectral problems of the Toeplitz and Laplace operator" (2015-2016, with the support of the Väisälä Foundation of the Finnish Academy of Sciences and Letters.
- "New Aspects of Spectra of Elliptic Contour Problems" (Academy of Finland 2017-2018)
- Research Grants, Faculty of Science, University of Helsinki (2017, 2018)
Responsible organizer of the following recent international conferences:
- Mathematical Methods for Spectral Problems: Applications to Waveguides, Periodic Media, and Metamaterials, Helsinki, March 5-7, 2013.
- Theory of operators and spaces of analytic functions, Helsinki, October 25-29, 2010.
- Functional analysis Valencia 2010(session organizer).
- Elliptical Edge Problem, Workshop, Helsinki, 12.6.2009
- Spaces of analytic functions, Joensuu, 29.5.-2.6.2006
- Nonlinear Parabolic Problems, Espoo, 10/17-21/2005
- Functional Analysis Workshop (ECM 2004 Stockholm Satellite Conference) Joensuu, 20.-24.6.2004
- Summer school "Function spaces and operator theory", Joensuu, May 19-23, 2003
- Functional Analysis and Related Topics, Helsinki, 1999
board member ofFinnish Mathematical Societyduring 1996-2011.
If you would like to take a closer look at some of my work, please contact me via email! here is the completeMailing listsince March 2018.
My research topics are functional analysis, operator theory and applications.The two main areas of application are elliptic spectral fringes and operator theory/harmonic analysis on spaces of analytic functions. There are also articles on parabolic PDEs, spatial structure of analytic functions and coherent packages of vector-valued analytic functions, invisibility in the linear theory of water waves, and stress quantization.
LATEST WORKS(Almost every):
- J. Bonet, W. Lusky, J. T.,On the restriction and compactness of the Toeplitz operators on weighted H^\infty spaces. Appears in J. Functional Anal.Abstract.
SA Nasarow, JT,The "flashing eigenvalues" of the Steklov problem produce the continuous spectrum in a cusp region. Appears in J. Differential EquationsAbstract.
V.Kozlov, J.T,Floquet problem and central manifold reduction for ordinary differential operators with periodic coefficients in Hilbert spaces.Abstract.
A. Karapetyants, JT,Toeplitz operators with radial symbols in weighted holomorphic Orlicz spaces. Theme.Abstract.
SA Nasarow, JT,Essential periodic average spectrum with scattered extraneous inclusions. To appear on Pure Appl. functional analysis.Abstract.
J. Bonet, W. Lusky, J. T.,Fixed kernels and fixed shells of weighted Bergman spacesBanach J. Math. Analysis. 13, 2 (2019), 468-485.Abstract.
J. Bonet, W. Lusky, J. T.,Distance formulas in weighted Banach spaces of analytic functions. anal complex. Operator T. 13.3 (2019), 893--900.Abstract.
S.A.Nazarov, N.Popoff, J.T,Robin Laplacean's plunging and blinking eigenvalues in a top domain. Appearing in Proc. Royal Society sect of Edinburgh. A math.Abstract.
SA Nasarow, JT,Essential spectrum of a periodic waveguide with non-periodic perturbation. J. Mathematics. Anal. Motion 463 (2018), 922-933.Abstract.
JT, J. Virtanen,On the compactness of Toeplitz operators in Bergman spaces. Functions Approximation 59.2 (2018), 305-318.Abstract.
G.Leugering, S.A.Nazarov, A.S.Slutskij, J.T,Asymptotic Analysis of a Thin Rod Clamp Connection. Appears on Z. Angew. Mathematics. Me ZAMM.Abstract.
J. Bonet, W. Lusky, J. T.,Schauder basis and decay rate of the heat equation. J. Evolution Equations, (2019)Abstract.
L.Chesnel, S.A.Nazarov, J.T,Surface waves in a channel with thin tunnels and bottom wells: non-reflective underwater topography. Appears in Anal Asymptotic.Abstract.
G.Leugering, S.A.Nazarov, J.T,Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides. asymptotic anus. 111, 2 (2019), 69-111.Abstract.
J. Bonet, W. Lusky, J. T.,Monomial basis in spaces of analytic functions of the Korenblum type. Proc.Amer.Math.Soc. 146, 12 (2018), 5269-5278Abstract
SA Nasarow, JT,Singularities at the contact point of two kissing Neumann spheres. J.Diff. Equations 264, 3 (2018), 1521-1549.Abstract.
V.Chiado Piat, S.A.Nazarov, J.T,Built-in eigenvalues for water waves in a three-dimensional channel with fine rendering. Quarterly J.Mech.Appl.Math. 71, 2 (2018), 187--220.Abstract.
SA Nasarow, JT,Pathology of essential spectra of elliptical problems in a periodic family of threaded balls with a radius tapering towards infinity. Theme.Abstract
J. Bonet, J. T.,Solid hulls of weighted Banach spaces of integer functions. Rev. Mat. Iberoamericana 34 (2018), 593-608.Abstract.
JT, K. Vilonen,Cartan's theorems for Stein manifolds on a discrete valuation basis. J.Geom.Analysis. 29.1 (2019), 577-615.Abstract.
In general, my recent work deals with very classical problems on spectra, eigenvalues and eigenfunctions of the Dirichlet/Neumann-Laplace operator in special areas such as periodic or perturbed periodic or in those with fine structures. We study general elliptic equations or systems or special ones such as elasticity or piezoelectricity. In another direction, there are a number of articles on various aspects of Toeplitz and other operators, on Bergman-like spaces, solid shells and other results on the structure of spaces of analytic functions, invisibility in the linear theory of water waves, etc. .
PARTIAL DIFFERENTIAL EQUATION TOPICS:
- Contour problems for elliptical PDEs.
- 1.Spectrum of the Neumann/Dirichlet problemfor elliptic equations or systems in geometrically fascinating areas.
SA Nasarow, JT,Essential periodic average spectrum with scattered extraneous inclusions.To appear on Pure Appl. functional analysis.
S.A.Nazarov, N.Popoff, J.T,Robin Laplacean's plunging and blinking eigenvalues in a top domain.Appearing in Proc. Royal Society sect of Edinburgh. A math.
SA Nasarow, JT,Essential spectrum of a periodic waveguide with non-periodic perturbation.J.Math.Anal.Appl.463 (2018), 922-933.
SA Nasarow, JT,Singularities at the contact point of two kissing Neumann spheres.J.Diff.Equations 264, 3 (2018), 1521-1549.
SA Nasarow, JT,Pathology of essential spectra of elliptical problems in periodic families of beads strung with radius narrowing to infinity.Theme.
F. Bakharev, G. Cardone, S. A. Nazarov, J. T.,Effects of Rayleigh waves on essential spectra in the composite periodic plane.Integral Eq.Oper.Theory. 88 (2017), 373--386.
G.Cardone, S.A.Nazarov, J.T,Spectra of open waveguides in periodic media.Functional Analysis Journal 269 (2015), 2328-2364.
S.A. Nazarov, E. Pérez, J.T.,Location effect for Dirichlet eigenfunctions in non-smooth thin domains.AMS Transactions 368 (2016), 4787-4829.
F. Ferraresso, JT,Dirichlet problem with singular perturbation on a biperiodic perforated planeAnn.Univ.Ferrara 61 (2015), 1216-1225
G.Leugering, S.A.Nazarov, J.T,Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides.asymptotic anus. 111, 2 (2019), 69-111. Abstract..
F. Bacharew, JT,Bands in the spectrum of a periodic elastic waveguideRevista Angew.Math.Phys. 68 (2017)
SA Nasarow, JT,Elastic and piezoelectric waveguides can have infinite holes in their spectra,Mechanical reports. 344 (2016), 190-194.
SA Nasarow, JT,Spectral holes for periodic piezoelectric waveguides.Revista Angew.Math.Phys. 66 (2015), 3017-3047
SA Nazarov, A. S. Slutskij, JT,Korn's inequality for a thin rod with rounded ends.Math.Methoden Appl.Sci. 37, 16 (2014), 2463-2483
G.Cardone, S.A.Nazarov, J.T,A criterion for the existence of the essential spectrum for pointed elastic bodies.J. Math. pure. Application 92, 6 (2009), 628-650.
DU. Nazarov, K. Suotsalainen, JT,The essential spectrum of a periodic elastic waveguide can contain any number of holes.Applicable Analysis. 89.1 (2010), 109-124.
L.Chesnel, S.A.Nazarov, J.T,Surface waves in a channel with thin tunnels and bottom wells: non-reflective underwater topography.Appears in Anal Asymptotic.
V.Chiado Piat, S.A.Nazarov, J.T,Built-in eigenvalues for water waves in a three-dimensional channel with fine rendering.Trimestral J.Mech.Appl.Math. 71, 2 (2018), 187--220.
SA Nasarow, JT,Radiation conditions for the linear problem of water waves in periodic channels.Appears in Math.
A.-S.Bonnet-BenDhia, S.A.Nazarov, J.T,Invisible underwater survey for surface waves at certain frequenciesWave Motion 57 (2015), 129-142.
F. Bakharev, K. Ruotsalainen, J. T.,Spectral holes for the model of linear surface waves in periodic channels.Quarterly J.Mech.Appl.Math. 67, 3 (2014), 343-362
J. Martín, S.A. Nasarow, JT,Spectrum of the linear water model for a two-layer liquid with cusp geometries at the interfaceZ.Angew.Math.Mech. 1-18 (2014)
SA Nasarow, JT,Spectral properties in John's problem about a free-floating submerged body in a finite basinDifferential Equation 49, 12 (2013), 1544-1559
SA Nasarow, JT,Location estimates for appropriate frequencies of waves caught by free-floating bodies in the channel.SIAM J.Math.Anal. 45, 4 (2013), 2523-2545
- 1. Long-term asymptotics oflinear and semilinear diffusion equations..
- J. Bonet, W. Lusky, J. T.,Schauder basis and decay rate of the heat equation.J. Evolution Equations, (2019).
JT,Long-term asymptotics of subliminal solutions of a semilinear Cauchy problem.Dif.Gl.Apl. 3,2 (2011), 279-297
JT,Asymptotic behavior of a semilinear diffusion equation.J.Evol.Equations 7,3 (2007), 429-447 - 2.Cahn-Hilliard equation.
- T.Korvola, A.Kupiainen, J.T,Anomalous scaling for 3D Cahn-Hilliard fronts.with. Pure application. Mathematics 58, (2005), 1077-1115.
J.Bricmont, A.Kupiainen, J.T,Stability of the Cahn-Hilliard frontsComm.Pure.Appl.Math. LII (1999), 839-871. - 3.Gradientenexplosion.
- M.Fila, J.T, M.Winkler,Convergence to a singular steady state of a parabolic gradient equation.Appl.Math.Letters 20 (2007), 578-582.
TOPICS TO CLEAR THE ANALYTICAL FUNCTION:
- Building analytical function spaces and packages
- 1. Structure of the spaces of analytic functions.
- J. Bonet, W. Lusky, J. T.,Fixed kernels and shells of weighted Bergman spacesBanach J. Mathematics. Analysis. 13, 2 (2019), 468-485.
J. Bonet, W. Lusky, J. T.,Monomial basis in spaces of analytic functions of the Korenblum type.Proc.Amer.Math.Soc. 146, 12 (2018), 5269-5278
J. Bonet, W. Lusky, J. T.,Distance formulas in weighted Banach spaces of analytic functions.anal complex. Operator T. 13.3 (2019), 893-900.
J. Bonet, W. Lusky, J. T.,Solid hulls and cores with a density of $H^\infty$.Rev. Matt. Compensation 31 (2018), 781-804.
J. Bonet, J. T.,Solid hulls of weighted Banach spaces of analytic functions on the unit disk with exponential weights.Ann.Acad.Sci.Fenn. 43 (2018), 521-530
J. Bonet, J. T.,Solid hulls of weighted Banach spaces of integer functions.Pfr. Matt. Iberoamericana 34 (2018), 593-608.
- 2. Coherent Analysis Packages: Extension of Cartan's A and B Theorems.
- JT, K. Vilonen,Cartan's theorems for Stein manifolds on a discrete valuation basis.J. Geometrisches Anal. 29.1 (2019), 577-615
- Toeplitz and other linear operators
- 1.Toeplitz operators on Bergman spaces:Constraint, compactness and Fredholm properties.
- J. Bonet, W. Lusky, J. T.,On the restriction and compactness of the Toeplitz operators on weighted H^\infty spaces.Appears in J. Functional Anal.
A. Karapetyants, JT,Toeplitz operators with radial symbols in weighted holomorphic Orlicz spaces.Theme.
JT, J. VirtanenOn the compactness of Toeplitz operators in Bergman spaces.Functional approach 59.2 (2018), 305-318.
JT, J. Virtanen,About generalized Toeplitz and little Hankel operators on Bergman spaces.No archive Math appears.
A. Perälä, J. T., J. Virtanen,Toeplitz operators of Dirichlet-Besov spaces.To appear on Houston J.Math.
J. Bonet, J. T.,A note on Volterra operators on weighted Banach spaces of integer functionsMatemáticas Nachrichten 288 (2015), 1216-1225.
A. Perälä, J. T., J. Virtanen,New results and open problems on Toeplitz operators in Bergman spacesNew York J. Mathematik. 17a (2011), 147-164.
A. Perälä, J. T., J. Virtanen,Toeplitz operators with distribution symbols in jib spaces.Function and ca. 44.2 (2011), 203-213.
W.Lusky, JT,Toeplitz operators in Bergman spaces and Hardy multipliers.study mathematics. 204 (2011), 137-154.
JT, J. Virtanen,Weighted BMO and Toeplitz operators in Bergman's A¹ space.J. Operator Th. 68 (2012), 131-140.
A. Perälä, J. T., J. Virtanen,Toeplitz operators with distribution symbols in Bergman spaces.Proc. Edinburgh Math. Soc. 54, 2 (2011), 505-514.
JT, J. Virtanen,Toeplitz operators in Bergman spaces with locally integrable symbols.Rev.Math.Iberoamericana 26,2 (2010), 693-706.
- 2. Toeplitz Operators ulocally convex spaces.
- J. Bonet, J. T.,Toeplitz operators in the space of analytic functions with logarithmic growth.J.Math.Anal.Appl. 353 (2009), 428-435.
M. Englis, JT,Deformation quantization and Borel's theorem in locally convex spaces.study mathematics. 180.1 (2007), 77-93.
- Bergman projections
- 1.Weighted estimates of sup.
- P.Erkkilä, J.T,Supernormal estimates for Bergman projections in regulated areas.Mathematical.Scanning. 102, 1 (2008), 111-130.
J. Bonet, M. Englis, J. T.,Weighted estimates of L∞ for Bergman projections.Studia Math.171,1 (2005), 67-92.
M.English, T.Hänninen, J.T,Minimal spaces of type L∞ in strictly pseudoconvex regions where the Bergman projection is continuous.Houston J. Mathematik. 32.1 (2006)
JT,On the continuity of the Bergman and Szegö projections.Houston J. Mathematik. 30.1 (2004), 171-190.
- 2. General projections forlose weight quickly.
- W.Lusky, JT,On weighted spaces of holomorphic functions of several variables.Israel J. Mathematics. 176.1 (2010), 381-399.
W.Lusky, JT,Connected holomorphic projections for exponentially decreasing weights.J. Application of function spaces. 6, 1 (2008), 59-70.
- composition operators
- composition operators inBloch type spaces and classes of hyperbolic functions.
- F. Perez-Gonzales, J. Rättyä, J.T,Continuous and compact Lipschitz composition operators in hyperbolic classes.Mediterranean J. Math. 8.1 (2011), 123-135.
O.Blasco, M.Lindström, J.T,Compositions from Bloch to BMOA in multiple complex variables.Var complex. Application Theory 50, 14 (2005), 1061-1080.
SELECTION OF ARTICLES ON DIFFERENT TOPICS FUNCTIONAL ANALYSIS:
- Weighted inductive limits of integer functions (K.D.Bierstedt, J.Bonet,J.Taskinen).Monatshefte Math.154, 2 (2008), 103-120.
Regularly decreasing weights and the topological subspace problem.Mathematics. Messrs. 278, 10 (2005), 1-8.
The essential norm of the Bloch composition operators on Qp (M.Lindström, S.Makhmutov, J.Taskinen).Can.Math.Bull. 47,2(2004), 49-59.
Review of the subspace problem for weighted inductive limits. (J Bonet, J Taskinen)Rocky Mountain Mathematics.J. 30, 1 (2000), 85-99.
Composition operators between weighted Banach spaces of analytic functions (J.Bonet, P.Domanski, M.Lindström, J.Taskinen).J. Austr. Mathematics. Society (serial number A) 64 (1998), 101-118.
Weights and associated spaces of holomorphic functions (K.D.Bierstedt, J.Bonet, J.Taskinen).study mathematics. 127, 2 (1998), 137-168.
Compact composition operators on general weighted spaces.Houston J. Mathematik. 27 (2001), 203-218.
Linearization of holomorphic maps in C(K) spaces.Isr.J.Math. 92 (1995), 207-219.
An application of averaging operators to multilinearity.Mathematics. Annals 297.3 (1993), 567-572.
A continuous surjection of the unit interval to the unit square. Rev. Matte. universityComplutense Madrid 6.1 (1993), 101-120.
A based Fre\'echet-Schwartz space that has a complementary non-based subspace.perc. america Mathematics. Society 113.1 (1991), 151-155.
Fréchet's undifferentiated functional spaces (J.Bonet, J.Taskinen).Bull. Roy society. Liege Science 58 , 483-490 (1989)
About the injective tensor product of (DF)-spaces (A.Defant, K.Floret, J.Taskinen).Arc. Mathematics. 57 , 149-154 (1991).
On a problem of infinite-dimensional holomorphic topologies (J.M. Ansemil, J.Taskinen).Arc. Mathematics. 54, 61-64 (1990)
(FBa) and (FBB) spaces.Mathematical Journal 198, 339-365 (1988)
The projective tensor product of Fréchet-Montel spaces.Studia Mathematica 91, 17-30 (1988).
Counterexamples to Grothendieck's "Probléme des topologies".Ana. academic science of the fenn ser. I Dis 63 (1986).
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FAQs
What is operator theory in functional analysis? ›
In contemporary mathematics, operator theory is a branch of functional analysis that focuses on bounded and unbounded maps from a normed vector space (or a topological vector space) into another.
What is the difference between operator and functional? ›Here are some differences between an operator and a function: An operator does not push its parameters onto the stack, but a function pushes its parameters onto the stack. The compiler knows about the operation of the operators, but is not aware of the output of the function.
Is functional analysis applied in math? ›Functional analysis is an abstract branch of mathematics that originated from classical anal- ysis. The impetus came from applications: problems related to ordinary and partial differential equations, numerical analysis, calculus of variations, approximation theory, integral equations, and so on.
Which tool is used for functional analysis? ›Protein Functional Analysis (PFA) tools are used to assign biological or biochemical roles to proteins. Protein Functional Analysis using the InterProScan program. PfamScan is used to search a FASTA sequence against a library of Pfam HMM. phmmer is used to search one or more sequences against a sequence database.
Why operator functions are used? ›An operator is used to manipulate individual data items and return a result. These items are called operands or arguments. Operators are represented by special characters or by keywords.
What are the 4 types of operators? ›- arithmetic operators.
- relational operators.
- logical operators.
The different types of operators are arithmetic operators, assignment operators, comparison operators, logical operators, identity operators, membership operators, and boolean operators.
What are the 5 different types of operators? ›- Logical Operators. Unary operators in C. Binary operators in C.
- Conditional Operator.
- Bitwise Operators.
- Special Operators.
Comparison Operators are used to perform comparisons. Concatenation Operators are used to combine strings. Logical Operators are used to perform logical operations and include AND, OR, or NOT. Boolean Operators include AND, OR, XOR, or NOT and can have one of two values, true or false.
What are the five conditions in a functional analysis? ›Functional Analysis (FAn)
Using a standard FAn, attention, demand, tangible, and alone conditions are compared to a play/recreational control condition (e.g., Iwata, Dorsey, Slifer, Bauman, & Richman, 1982/1994).
What are the four conditions of a functional analysis? ›
In a traditional FA there are four conditions: play (also known as the control condition), alone condition, contingent escape condition or demand, and contingent attention condition.
Why should I study functional analysis? ›Functional analysis plays a fundamental role in the theory of differential equations, particularly partial differential equations, representation theory, and probability.
What are the 3 steps of functional analysis? ›...
Note that these methods sometimes go by different names.
- Indirect Functional Assessments. ...
- Observational (Direct) Functional Assessments. ...
- Functional Analysis.
The three stages of functional analysis can provide a systematic means to identify a problem behavior, understand the triggers (antecedents) and consequences that maintain it, and then to introduce interventions.
What is the basic concept of function analysis? ›Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
What are the benefits of having operator functions that perform object conversion? ›First, they can be used to simplify code. For example, if you have a function that converts an object into a string, you can use an operator function to do the same job without having to write the code twice. Additionally, operator functions can be useful when you need to perform complex object conversions.
Why operator is faster than function? ›Are operators faster than functions? Calling a function at runtime is potentially slower than not calling a function. But, as we've found out, an operator can actually internally call a function. Besides, a function call for the abstract machine doesn't necessarily mean that a function will be called at runtime.
What are the six types of operators? ›- Arithmetic Operators.
- Assignment Operators.
- Relational Operators.
- Logical Operators.
- Bitwise Operators.
- Other Operators.
An operator is a symbol which operates on a variable or value. There are types of operators like arithmetic, logical, conditional, relational, bitwise, assignment operators etc. Some special types of operators are also present in C like sizeof(), Pointer operator, Reference operator etc.
What are examples of operators? ›Arithmetic Operator With Example
Arithmetic Operators are the operators which are used to perform mathematical calculations like addition (+), subtraction (-), multiplication (*), division (/), and modulus (%). It performs all the operations on numerical values (constants and variables).
What is an operator in set theory? ›
In Relational Algebra, Set theory operators are- Union operator, Intersection operator, Difference operator. Condition for using set theory operators- Both the relations must be union compatible.
What is an operator in operator theory? ›Operator theory is the branch of functional analysis which deals with bounded linear operators and their properties. It can be split crudely into two branches, although there is considerable overlap and interplay between them. These extend the spectral theory, for bounded operators.
What do you mean by operator function? ›An operator function is a user-defined function, such as plus() or equal(), that has a corresponding operator symbol. For an operator function to operate on the opaque data type, you must overload the routine for the opaque data type.
What is an operator in group theory? ›In abstract algebra, a branch of mathematics, the algebraic structure group with operators or Ω-group can be viewed as a group with a set Ω that operates on the elements of the group in a special way. Groups with operators were extensively studied by Emmy Noether and her school in the 1920s.