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 research projects supported by the Academy of Finland:

  • "Spectral analysis of boundary value problems in mathematical physics" (2012),
  • "Functional analysis and applications" (2010-2013),
  • "Mathematical models of pietzoelektric and elastic systems" (2013-2014)
  • "Spectrum of the piezoelectricity system" (2015-2016)
  • Also: "Spectral problems of Toeplitz and Laplace operators" (2015-2016), supported by the Väisälä Foundation of the Finnish Academy of Sciences and Letters.

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.

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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, deformation quantization, and most recently, on coherent sheafs of vector valued analytic functions.

SOME MOST RECENT WORKS:

J.T, K.Vilonen, Cartan theorems for Stein manifolds over a discrete valuation base. Here is an 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. Here is an abstract.
S.A.Nazarov, J.T, Singularities at the contact point of two kissing Neumann balls. Submitted. Here is an abstract.
J.Bonet, J.T, Solid hulls of weighted Banach spaces of entire functions. To appear in Rev.Mat.Iberoamericana. Here is an abstract.
J.T, J. Virtanen On generalized Toeplitz and little Hankel operators on Bergman spaces. Submitted. Here is an abstract.

Other recent works concern quite classical problems on spectra and eigenfunctions of the Dirichlet/Neumann Laplacian, spectra of open waveguides, an invisibility result for the linear water-wave equation, and various aspects of Volterra and Toeplitz operators on Bergman-type spaces.


TOPICS ON PARTIAL DIFFERENTIAL EQUATIONS:

  • Boundary problems for elliptic PDE's.
    1. Spectrum of the Neumann problem for elliptic equations or systems in geometrically intriguing domains.
    S.A.Nazarov, J.T, Singularities at the contact point of two kissing Neumann balls. Submitted.
    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, Particular Rayleigh waves in composite plane. Submitted.
    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
    S.A.Nazarov, J.T, Structure of the Spectrum of a Periodic Family of Identical Cells Connected by Converging Apertures J.Math.Sci.194, 1 (2013), 72-82.
    S.A.Nazarov, J.T, Spectral Anomalies of the Robin Laplacian in Non-Lipschitz Domains J.Math.Sci.Univ.Tokyo 20, 1 (2013), 27-90
    S.A.Nazarov, K.Ruotsalainen, J.T, Spectral gaps in the Dirichlet and Neumann problems on the plane perforated by a double-periodic family of cirular holes. J.Math.Sci. 181,2 (2012), 164-222.


    2. Spectral properties of the linear elasticity system.
    F.Bakharev, J.T, Bands in the spectrum of a periodic elastic waveguide Submitted.
    S.A.Nazarov, J.T, Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra, Comptes Rendus M\'ecanique. 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.
    V.Chiado Piat, S.A.Nazarov, J.T, Embedded eigenvalues for water-waves in a three dimensional channel with a thin screen. Submitted.
    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
    S.A.Nazarov, J.T, J.Videman, Asymptotic behaviour of interfacial trapped modes in a two-layer fluid. Wave Motion 50,2 (2013), 111-126
    S.A.Nazarov, J.T, Radiation conditions at the top of a rotational cusp in the theory of water-waves. Math. Model. Numer. Anal. 45,4 (2011), 947--979

  • Parabolic PDE's
    1. Long-time asymptotics of semilinear diffusion equations..
    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. 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. Manuscript, arXiv identifier 1609.03658
    2. Solid hulls of analytic function spaces.
    J.Bonet, J.T, Solid hulls of weighted Banach spaces of entire functions. To appear in Rev.Mat.Iberoamericana.
  • Toeplitz and Volterra operators
    1. Toeplitz operators on Bergman spaces: boundedness, compactness and Fredholm properties.
    J.T, J.Virtanen, On generalized Toeplitz and little Hankel operators on Bergman spaces. Submitted.
    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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