Helsingin Yliopisto

RESEARCH BY JARI TASKINEN

Functional analysis, operator theory and applications




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My affiliation is at the Department of Mathematics and Statistics of University of Helsinki (see also my Departmental homepage).

Recent supported research projects:

  • "Spectral analysis of boundary 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 the piezoelectricity system" (Academy of Finland 2015-2016)
  • "Spectral problems of Toeplitz and Laplace operators" (2015-2016, supported by the Väisälä Foundation of the Finnish Academy of Sciences and Letters.
  • "New aspects of spectra of elliptic boundary problems" (Academy of Finland 2017-2018)
  • Research grants, Faculty of Science of the University of Helsinki (2017, 2018)

Responsible organizer of the following recent international conferences:

Member of the Board of the Finnish Mathematical Society during 1996-2011.

If you want to have a closer look at some of my papers, please contact me by e-mail! Here is the complete list of publications as of March 2018.

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My research topic is functional analysis, operator theory and applications. The two main application areas are spectral elliptic boundary problems and operator theory / harmonic analysis in analytic function spaces. There are also works on parabolic PDE's, structure of analytic function spaces and coherent sheafs of vector valued analytic functions, invisibility in linear water wave theory, and deformation quantization.

RECENT WORKS (nearly all of them):

J.Bonet, W.Lusky, J.T, On boundedness and compactness of Toeplitz operators in weighted H^\infty-spaces. To appear in J. Functional Anal. Abstract.
S.A.Nazarov, J.T, "Blinking eigenvalues" of the Steklov problem generate the continuous spectrum in a cuspidal domain. To appear in J. Differential Equations Abstract.
V.Kozlov, J.T, Floquet problem and center manifold reduction for ordinary differential operators with periodic coefficients in Hilbert spaces To appear. Abstract.
A.Karapetyants, J.T, Toeplitz operators with radial symbols on weighted holomorphic Orlicz spaces. Submitted. Abstract.
S.A.Nazarov, J.T, Essential spectrum of periodic medium with sparsely placed foreign inclusions. To appear in Pure Appl. Functional Anal. Abstract.
J.Bonet, W.Lusky, J.T, Solid cores and solid hulls of weighted Bergman spaces Banach J. Math. Analysis. 13, 2 (2019), 468--485. Abstract.
J.Bonet, W.Lusky, J.T, Distance formulas on weighted Banach spaces of analytic functions. Complex Anal. Operator Th. 13,3 (2019), 893--900. Abstract.
S.A.Nazarov, N.Popoff, J.T, Plummeting and blinking eigenvalues of the Robin Laplacian in a cuspidal domain. To appear in Proc. Royal Soc. Edinburgh Sect. A Mathematics. Abstract.
S.A.Nazarov, J.T, Essential spectrum of a periodic waveguide with non-periodic perturbation. J. Math. Anal. Appl.463 (2018), 922-933. Abstract.
J.T, J.Virtanen, On compactness of Toeplitz operators in Bergman spaces. Functiones Approximatio 59.2 (2018), 305-318. Abstract.
G.Leugering, S.A.Nazarov, A.S.Slutskij, J.T, Asymptotic analysis of a bit brace shaped junction of thin rods. To appear in Z. Angew. Math. Mech 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 wells at the bottom: non-reflecting underwater topography. To appear in Asymptotic Anal. Abstract.
G.Leugering, S.A.Nazarov, J.T, Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides. Asymptotic Anal. 111, 2 (2019), 69-111. Abstract.
J.Bonet, W.Lusky, J.T, Monomial basis in Korenblum type spaces of analytic functions. Proc.Amer.Math.Soc. 146, 12 (2018), 5269-5278 Abstract
S.A.Nazarov, J.T, Singularities at the contact point of two kissing Neumann balls. J.Diff.Equations 264, 3 (2018), 1521-1549. Abstract.
V.Chiado Piat, S.A.Nazarov, J.T, Embedded eigenvalues for water-waves in a three dimensional channel with a thin screen. Quarterly J.Mech.Appl.Math. 71, 2 (2018), 187--220. Abstract.
S.A.Nazarov, J.T, Pathology of essential spectra of elliptic problems in periodic family of beads threaded by a spoke thinning at infinity. Submitted. Abstract
J.Bonet, J.T, Solid hulls of weighted Banach spaces of entire functions. Rev.Mat.Iberoamericana 34 (2018), 593--608. Abstract.
J.T, K.Vilonen, Cartan theorems for Stein manifolds over a discrete valuation base. J.Geom.Analysis. 29,1 (2019), 577--615. Abstract.

In general, my recent works concern quite classical problems on spectra, eigenvalues and eigenfunctions of the Dirichlet/Neumann Laplacian on special domains like periodic or perturbed periodic ones, or on those with thin structures. We study general elliptic equations or systems, or special ones like elasticity or piezoelectricity. In another direction, there are a number of papers on various aspects of Toeplitz and other operators on Bergman-type spaces, solid hulls and other results on the structure of analytic function spaces, invisibility in the linear water-wave theory, etc.


TOPICS ON PARTIAL DIFFERENTIAL EQUATIONS:

  • Boundary problems for elliptic PDE's.
    1. Spectrum of the Neumann/Dirichlet problem for elliptic equations or systems in geometrically intriguing domains.
    V.Kozlov, J.T, Floquet problem and center manifold reduction for ordinary differential operators with periodic coefficients in Hilbert spaces To appear.
    S.A.Nazarov, J.T, Essential spectrum of periodic medium with sparsely placed foreign inclusions. To appear in Pure Appl. Functional Anal.
    S.A.Nazarov, N.Popoff, J.T, Plummeting and blinking eigenvalues of the Robin Laplacian in a cuspidal domain. To appear in Proc. Royal Soc. Edinburgh Sect. A Mathematics.
    S.A.Nazarov, J.T, Essential spectrum of a periodic waveguide with non-periodic perturbation. J.Math.Anal.Appl.463 (2018), 922-933.
    S.A.Nazarov, J.T, Singularities at the contact point of two kissing Neumann balls. J.Diff.Equations 264, 3 (2018), 1521-1549.
    S.A.Nazarov, J.T, Pathology of essential spectra of elliptic problems in periodic family of beads threaded by a spoke thinning at infinity. Submitted.
    F.Bakharev, G.Cardone, S.A.Nazarov, J.T, Effects of Rayleigh waves to essential spectra in 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. Journal of Functional Analysis 269(2015), 2328-2364.
    S.A.Nazarov, E.Peréz, J.T, Localization effect for Dirichlet eigenfunctions in thin non-smooth domains. Transactions A.M.S. 368 (2016), 4787-4829.
    F.Ferraresso, J.T, Singular perturbation Dirichlet problem in a double-periodic perforated plane Ann.Univ.Ferrara 61 (2015), 1216-1225


    2. Spectral properties of the linear elasticity and piezoelectricity systems.
    G.Leugering, S.A.Nazarov, A.S.Slutskij, J.T, Asymptotic analysis of a bit brace shaped junction of thin rods. To appear in Z. Angew. Math. Mech ZAMM.
    G.Leugering, S.A.Nazarov, J.T, Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides. Asymptotic Anal. 111, 2 (2019), 69-111. Abstract..
    F.Bakharev, J.T, Bands in the spectrum of a periodic elastic waveguide Zeitschrift Angew.Math.Phys. 68 (2017)
    S.A.Nazarov, J.T, Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra, Comptes Rendus Mécanique. 344 (2016), 190--194.
    S.A.Nazarov, J.T, Spectral gaps for periodic piezoelectric waveguides. Zeitschrift Angew.Math.Phys. 66 (2015), 3017-3047
    S.A.Nazarov, A.S.Slutskij, J.T, Korn inequality for a thin rod with rounded ends. Math.Methods Appl.Sci. 37, 16 (2014), 2463-2483
    G.Cardone, S.A.Nazarov, J.T, A criterion for the existence of the essential spectrum for beak-shaped elastic bodies. J.Math. Pur. Appl. 92, 6 (2009), 628–650.
    S.A.Nazarov, K.Ruotsalainen, J.T, Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps. Applicable Anal. 89,1 (2010), 109-124.


    3. Spectral problems with Steklov boundary condtions.
    S.A.Nazarov, J.T, "Blinking eigenvalues" of the Steklov problem generate the continuous spectrum in a cuspidal domain. Submitted.
    L.Chesnel, S.A.Nazarov, J.T, Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater topography. To appear in Asymptotic Anal.
    V.Chiado Piat, S.A.Nazarov, J.T, Embedded eigenvalues for water-waves in a three dimensional channel with a thin screen. Quarterly J.Mech.Appl.Math. 71, 2 (2018), 187--220.
    S.A.Nazarov, J.T, Radiation conditions for the linear water-wave problem in periodic channels. To appear in Math.Nachr.
    A.-S.Bonnet-BenDhia, S.A.Nazarov, J.T, Underwater topography invisible for surface waves at given frequencies Wave Motion 57 (2015), 129-142.
    F.Bakharev, K.Ruotsalainen, J.T, Spectral gaps for the linear surface wave model in periodic channels. Quaterly J.Mech.Appl.Math. 67, 3 (2014), 343-362
    J.Martin, S.A.Nazarov, J.T, Spectrum of the linear water model for a two-layer liquid with cuspidal geometries at the interface Z.Angew.Math.Mech. 1-18 (2014)
    S.A.Nazarov, J.T, Properties of the Spectrum in the John Problem on a Freely Floating Submerged Body in a Finite Basin Differential Eq. 49, 12 (2013), 1544-1559
    S.A.Nazarov, J.T, Localization estimates for eigenfrequences of waves trapped by freely floating body in channel. SIAM J.Math.Anal. 45, 4 (2013), 2523-2545

  • Parabolic PDE's
    1. Long-time asymptotics of linear and semilinear diffusion equations..
    J.Bonet, W.Lusky, J.T, Schauder basis and decay rate of the heat equation. J. Evolution Equations, (2019).
    J.T, Long time asymptotics of sub-threshold solutions of a semilinear Cauchy problem. Diff.Eq.Appl. 3,2 (2011), 279-297
    J.T, Asymptotical behaviour 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. Comm. Pure Appl. Math. LVIII, (2005), 1077-1115.
    J.Bricmont, A.Kupiainen, J.T, Stability of Cahn-Hilliard fronts Comm.Pure.Appl.Math. LII (1999), 839-871.
    3. Gradient blow-up.
    M.Fila, J.T, M.Winkler, Convergence to a singular steady state of a parabolic equation with gradient. Appl.Math.Letters 20 (2007), 578-582.

TOPICS ON ANALYTIC FUNCTION SPACES:

  • Structure of analytic function spaces and sheaves
    1. Structure of analytic function spaces.
    J.Bonet, W.Lusky, J.T, Solid cores and solid hulls of weighted Bergman spaces Banach J. Math. Analysis. 13, 2 (2019), 468--485.
    J.Bonet, W.Lusky, J.T, Monomial basis in Korenblum type spaces of analytic functions.Proc.Amer.Math.Soc. 146, 12 (2018), 5269-5278
    J.Bonet, W.Lusky, J.T, Distance formulas on weighted Banach spaces of analytic functions.Complex Anal. Operator Th. 13,3 (2019), 893-900.
    J.Bonet, W.Lusky, J.T, Solid hulls and cores of weighted $H^\infty$-spaces. Rev. Mat. Compl. 31 (2018), 781-804.
    J.Bonet, J.T, Solid hulls of weighted Banach spaces of analytic functions on the unit disc with exponential wieghts. Ann.Acad.Sci.Fenn. 43 (2018), 521-530
    J.Bonet, J.T, Solid hulls of weighted Banach spaces of entire functions. Rev.Mat.Iberoamericana 34 (2018), 593-608.
    2. Coherent analytic sheaves: extension of the Cartan theorems A and B.
    J.T, K.Vilonen, Cartan theorems for Stein manifolds over a discrete valuation base. J.Geometric Anal. 29,1 (2019), 577-615
  • Toeplitz and other linear operators
    1. Toeplitz operators on Bergman spaces: boundedness, compactness and Fredholm properties.
    J.Bonet, W.Lusky, J.T, On boundedness and compactness of Toeplitz operators in weighted H^\infty-spaces. To appear in J. Functional Anal.
    A.Karapetyants, J.T, Toeplitz operators with radial symbols on weighted holomorphic Orlicz spaces. Submitted.
    J.T, J.Virtanen On compactness of Toeplitz operators in Bergman spaces. Functiones Approximatio 59.2 (2018), 305-318.
    J.T, J.Virtanen, On generalized Toeplitz and little Hankel operators on Bergman spaces. To appear in Archiv Math.
    A.Perälä, J.T, J.Virtanen, Toeplitz operators of Dirichlet-Besov spaces. To appear in Houston J.Math.
    J.Bonet, J.T, A note about Volterra operators on weighted Banach spaces of entire functions Math. Nachrichten 288 (2015), 1216-1225.
    A.Perälä, J.T, J.Virtanen, New results and open problems on Toeplitz operators in Bergman spaces New York J. Math. 17a (2011), 147-164.
    A.Perälä, J.T, J.Virtanen, Toeplitz operators with distributional symbols on Fock spaces. Funct. et approx. 44,2 (2011), 203-213.
    W.Lusky, J.T, Toeplitz operators on Bergman spaces and Hardy multipliers. Studia Math. 204 (2011), 137-154.
    J.T, J.Virtanen, Weighted BMO and Toeplitz operators on the Bergman space A¹. J. Operator Th. 68 (2012), 131-140.
    A.Perälä, J.T, J.Virtanen, Toeplitz operators with distributional symbols on Bergman spaces. Proc.Edinburgh Math.Soc. 54, 2 (2011), 505-514.
    J.T, J.Virtanen, Toeplitz operators on Bergman spaces with locally integrable symbols. Rev.Math.Iberoamericana 26,2 (2010), 693-706.
    2. Toeplitz operators and locally convex spaces.
    J.Bonet, J.T, Toeplitz-operators on the space of analytic functions with logarithmic growth. J.Math.Anal.Appl. 353 (2009), 428-435.
    M.Engliš, J.T, Deformation quantization and Borel's theorem in locally convex spaces. Studia Math. 180,1 (2007), 77-93.

  • Bergman-type projections
    1. Weighted sup-norm estimates.
    P.Erkkilä, J.T, Sup-norm estimates for Bergman projections on regulated domains. Math.Scand. 102, 1 (2008), 111-130.
    J.Bonet, M.Engliš, J.T, Weighted L∞-estimates for Bergman projections. Studia Math.171,1 (2005), 67-92.
    M.Engliš, T.Hänninen, J.T, Minimal L∞-type spaces on strictly pseudoconvex domains on which the Bergman projection is continuous. Houston J. Math. 32,1 (2006)
    J.T, On the continuity of the Bergman and Szegö projections. Houston J.Math. 30,1 (2004), 171-190.
    2. General projections for rapidly decreasing weights.
    W.Lusky, J.T, On weighted spaces of holomorphic functions of several variables. Israel J.Math. 176,1 (2010), 381-399.
    W.Lusky, J.T, Bounded holomorphic projections for exponentially decreasing weights. J. Function Spaces Appl. 6, 1 (2008), 59-70.

  • Composition operators
    Composition operators on Bloch-type spaces and hyperbolic function classes.
    F.Perez-Gonzales, J.Rättyä, J.T, Lipschitz continuous and compact composition operators on hyperbolic classes. Mediterranean J.Math. 8,1 (2011), 123-135.
    O.Blasco, M.Lindström, J.T, Bloch-to-BMOA compositions in several complex variables. Complex Var. Theory Appl. 50, 14 (2005), 1061-1080.

SELECTION OF PAPERS ON VARIOUS TOPICS IN FUNCTIONAL ANALYSIS:

    Weighted inductive limits of entire functions (K.D.Bierstedt, J.Bonet,J.Taskinen). Monatshefte Math. 154, 2 (2008), 103-120.
    Regularly decreasing weights and the topological subspace problem. Math. Nachr.278, 10 (2005), 1-8.
    The essential norm of Bloch-to-Qp composition operators (M.Lindström, S.Makhmutov, J.Taskinen). Can.Math.Bull. 47,2 (2004), 49-59.
    Subspace problem for weighted inductive limits revisited. (J.Bonet, J.Taskinen) Rocky Mountain Math.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. Math. Soc. (Ser. A) 64 (1998), 101-118.
    Associated weights and spaces of holomorphic functions (K.D.Bierstedt, J.Bonet, J.Taskinen). Studia Math. 127, 2 (1998), 137-168.
    Compact composition operators on general weighted spaces. Houston J.Math. 27 (2001), 203-218.
    Linearization of holomorphic mappings on C(K)-spaces. Isr.J.Math. 92 (1995), 207-219.
    An application of averaging operators to multilinearity. Math. Annalen 297.3 (1993), 567-572.
    A continuous surjection from the unit interval onto the unit square. Rev. Mat. Univ. Complutense Madrid 6.1 (1993), 101-120.
    A Fr\'echet-Schwartz space with basis having a complemented subspace without basis. Proc. Amer. Math. Soc. 113,1 (1991), 151-155.
    Non-distinguished Fréchet function spaces (J.Bonet, J.Taskinen). Bull. Soc. Roy. Sci. Liége 58, 483-490 (1989)
    On the injective tensor product of (DF)-spaces (A.Defant, K.Floret, J.Taskinen). Arch. Math. 57, 149-154 (1991).
    On a problem of topologies in infinite dimensional holomorpy (J.M. Ansemil, J.Taskinen). Arch. Math. 54, 61-64 (1990)
    (FBa)- and (FBB)-spaces. Mathematische Zeitschrift 198, 339-365 (1988)
    The Projective Tensor Product of Fréchet-Montel Spaces. Studia Mathematica 91, 17-30 (1988).
    Counterexamples to "Probléme des topologies" of Grothendieck. Ann. Acad. Sci. Fenn. Ser. A I. Diss. 63 (1986).

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