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 20102013),

"Mathematical models of piezoelectric and elastic systems" (Academy of Finland 20132014)

"Spectrum of the piezoelectricity system" (Academy of Finland 20152016)
 "Spectral problems of Toeplitz and Laplace operators" (20152016, supported by the Väisälä Foundation
of the Finnish Academy of Sciences and Letters.

"New aspects of spectra of elliptic boundary problems" (Academy of Finland 20172018)

Research grants, Faculty of Science of the 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 5th7th, 2013.

Operator Theory and Analytic Function Spaces,
Helsinki, October 25th29th, 2010.

Functional Analysis Valencia 2010 (session organizer).
 Elliptic boundary problems, workshop, Helsinki, 12.6.2009
 Analytic function spaces, Joensuu, 29.5.2.6.2006
 Nonlinear parabolic problems, Espoo, 17.21.10.2005
 Functional analysis workshop (satellite conference of
ECM 2004 Stockholm) Joensuu, 20.24.6.2004
 Summer school "Function spaces and operator theory", Joensuu,
19.23.5.2003
 Functional analysis and related topics, Helsinki, 1999
Member of the Board of the
Finnish Mathematical Society during 19962011.
If you want to have a closer look at some of my papers,
please contact me by email! Here is the complete
list of publications
as of March 2018.

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^\inftyspaces. 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), 468485.
Abstract.
J.Bonet, W.Lusky, J.T,
Distance formulas on weighted Banach spaces of analytic functions.
Complex Anal. Operator Th.
13,3 (2019), 893900.
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 nonperiodic
perturbation. J. Math. Anal. Appl.463 (2018), 922933.
Abstract.
J.T, J.Virtanen, On compactness of Toeplitz operators in Bergman spaces. Functiones Approximatio 59.2 (2018), 305318.
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: nonreflecting underwater topography.
To appear in Asymptotic Anal.
Abstract.
G.Leugering, S.A.Nazarov, J.T, UmovPoyntingMandelstam radiation conditions in periodic composite piezoelectric waveguides.
Asymptotic Anal. 111, 2 (2019), 69111.
Abstract.
J.Bonet, W.Lusky, J.T, Monomial basis in Korenblum type spaces of analytic functions. Proc.Amer.Math.Soc. 146, 12 (2018), 52695278
Abstract
S.A.Nazarov, J.T, Singularities at the contact point of two kissing Neumann balls.
J.Diff.Equations 264, 3 (2018), 15211549.
Abstract.
V.Chiado Piat, S.A.Nazarov, J.T, Embedded eigenvalues for waterwaves in a three dimensional channel
with a thin screen. Quarterly J.Mech.Appl.Math. 71, 2 (2018), 187220.
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), 593608.
Abstract.
J.T, K.Vilonen, Cartan theorems for Stein manifolds over a discrete valuation base. J.Geom.Analysis. 29,1 (2019), 577615.
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 Bergmantype spaces, solid hulls and other results on the
structure of analytic function spaces, invisibility in the linear waterwave 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 nonperiodic
perturbation. J.Math.Anal.Appl.463 (2018), 922933.
S.A.Nazarov, J.T,
Singularities at the contact point of two kissing Neumann balls.
J.Diff.Equations 264, 3 (2018), 15211549.
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), 373386.
G.Cardone, S.A.Nazarov, J.T, Spectra of open waveguides in periodic media.
Journal of Functional Analysis 269(2015), 23282364.
S.A.Nazarov, E.Peréz, J.T, Localization effect for Dirichlet eigenfunctions in thin nonsmooth domains.
Transactions A.M.S. 368 (2016), 47874829.
F.Ferraresso, J.T, Singular perturbation Dirichlet problem in a doubleperiodic perforated plane
Ann.Univ.Ferrara 61 (2015), 12161225
 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, UmovPoyntingMandelstam radiation conditions in periodic
composite piezoelectric waveguides. Asymptotic Anal. 111, 2 (2019), 69111. 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), 190194.
S.A.Nazarov, J.T, Spectral gaps for periodic piezoelectric waveguides. Zeitschrift Angew.Math.Phys. 66 (2015), 30173047
S.A.Nazarov, A.S.Slutskij, J.T,
Korn inequality for a thin rod with rounded ends.
Math.Methods Appl.Sci. 37, 16 (2014), 24632483
G.Cardone, S.A.Nazarov, J.T,
A criterion for the existence of the essential spectrum
for beakshaped 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), 109124.

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: nonreflecting underwater topography.
To appear in Asymptotic Anal.
V.Chiado Piat, S.A.Nazarov, J.T, Embedded eigenvalues for waterwaves in a three
dimensional channel with a thin screen. Quarterly J.Mech.Appl.Math. 71, 2 (2018), 187220.
S.A.Nazarov, J.T, Radiation conditions for the linear waterwave
problem in periodic channels. To appear in Math.Nachr.
A.S.BonnetBenDhia, S.A.Nazarov, J.T, Underwater topography invisible for surface waves at given
frequencies
Wave Motion 57 (2015), 129142.
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), 343362
J.Martin, S.A.Nazarov, J.T, Spectrum of the linear water model for a twolayer liquid with cuspidal geometries at the interface
Z.Angew.Math.Mech. 118 (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), 15441559
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), 25232545
 Parabolic PDE's
 1. Longtime 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 subthreshold solutions of a semilinear
Cauchy problem.
Diff.Eq.Appl. 3,2 (2011), 279297
J.T, Asymptotical behaviour of a semilinear diffusion equation.
J.Evol.Equations 7,3 (2007), 429447
 2.
CahnHilliard equation.

T.Korvola, A.Kupiainen, J.T, Anomalous scaling for 3d CahnHilliard fronts.
Comm. Pure Appl. Math.
LVIII, (2005), 10771115.
J.Bricmont, A.Kupiainen, J.T, Stability of CahnHilliard fronts
Comm.Pure.Appl.Math. LII (1999), 839871.
 3.
Gradient blowup.

M.Fila, J.T, M.Winkler, Convergence to a singular steady state of
a parabolic equation with gradient.
Appl.Math.Letters 20 (2007), 578582.
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), 468485.
J.Bonet, W.Lusky, J.T, Monomial basis in Korenblum type spaces of analytic functions.Proc.Amer.Math.Soc. 146, 12 (2018), 52695278
J.Bonet, W.Lusky, J.T, Distance formulas on weighted Banach spaces of analytic functions.Complex Anal. Operator Th.
13,3 (2019), 893900.
J.Bonet, W.Lusky, J.T, Solid hulls and cores of weighted $H^\infty$spaces.
Rev. Mat. Compl. 31 (2018), 781804.
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), 521530
J.Bonet, J.T, Solid hulls of weighted Banach spaces of entire functions.
Rev.Mat.Iberoamericana 34 (2018), 593608.
 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), 577615

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^\inftyspaces. 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), 305318.
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 DirichletBesov 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), 12161225.
A.Perälä, J.T, J.Virtanen, New results and open problems on Toeplitz operators in Bergman spaces
New York J. Math. 17a (2011), 147164.
A.Perälä, J.T, J.Virtanen, Toeplitz operators with distributional symbols on Fock spaces.
Funct. et approx. 44,2 (2011), 203213.
W.Lusky, J.T, Toeplitz operators on Bergman spaces and Hardy multipliers.
Studia Math. 204 (2011), 137154.
J.T, J.Virtanen, Weighted BMO and Toeplitz operators on the
Bergman space A¹.
J. Operator Th. 68 (2012), 131140.
A.Perälä, J.T, J.Virtanen, Toeplitz operators with distributional symbols
on Bergman spaces.
Proc.Edinburgh Math.Soc. 54, 2 (2011), 505514.
J.T, J.Virtanen, Toeplitz operators on Bergman spaces with locally
integrable symbols.
Rev.Math.Iberoamericana 26,2 (2010), 693706.

2. Toeplitz operators and
locally convex spaces.

J.Bonet, J.T, Toeplitzoperators on the space of analytic functions with logarithmic
growth.
J.Math.Anal.Appl. 353 (2009), 428435.
M.Engliš, J.T, Deformation quantization and Borel's theorem in locally convex
spaces.
Studia Math. 180,1 (2007), 7793.

Bergmantype projections
 1. Weighted supnorm estimates.

P.Erkkilä, J.T, Supnorm estimates for Bergman projections on
regulated domains.
Math.Scand. 102, 1 (2008), 111130.
J.Bonet, M.Engliš, J.T, Weighted L∞estimates for Bergman projections.
Studia Math.171,1 (2005), 6792.
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), 171190.
 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), 381399.
W.Lusky, J.T, Bounded holomorphic projections for exponentially
decreasing weights.
J. Function Spaces Appl. 6, 1 (2008), 5970.
 Composition operators
 Composition operators on
Blochtype spaces and hyperbolic function classes.

F.PerezGonzales, J.Rättyä, J.T, Lipschitz continuous and compact composition operators on hyperbolic classes.
Mediterranean J.Math. 8,1 (2011), 123135.
O.Blasco, M.Lindström, J.T, BlochtoBMOA compositions in several complex
variables.
Complex Var. Theory Appl. 50, 14 (2005), 10611080.
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), 103120.
Regularly decreasing weights and the topological
subspace problem. Math. Nachr.278, 10 (2005), 18.
The essential norm of BlochtoQp composition
operators (M.Lindström, S.Makhmutov, J.Taskinen). Can.Math.Bull. 47,2
(2004), 4959.
Subspace problem for
weighted inductive limits
revisited. (J.Bonet, J.Taskinen) Rocky Mountain Math.J. 30, 1 (2000), 8599.
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), 101118.
Associated weights and spaces of holomorphic functions
(K.D.Bierstedt, J.Bonet, J.Taskinen).
Studia Math. 127, 2 (1998), 137168.
Compact composition operators on general weighted
spaces. Houston J.Math. 27 (2001), 203218.
Linearization of holomorphic mappings on C(K)spaces.
Isr.J.Math. 92 (1995), 207219.
An application of averaging operators to multilinearity.
Math. Annalen 297.3 (1993), 567572.
A continuous surjection from the unit interval onto
the unit square. Rev. Mat. Univ.
Complutense Madrid 6.1 (1993), 101120.
A Fr\'echetSchwartz space with basis having a complemented
subspace without basis. Proc. Amer. Math. Soc. 113,1
(1991), 151155.
Nondistinguished Fréchet function spaces
(J.Bonet, J.Taskinen).
Bull. Soc. Roy. Sci. Liége 58, 483490 (1989)
On the injective tensor product of (DF)spaces
(A.Defant, K.Floret, J.Taskinen).
Arch. Math. 57, 149154
(1991).
On a problem of topologies in infinite dimensional holomorpy
(J.M. Ansemil, J.Taskinen). Arch. Math. 54, 6164
(1990)
(FBa) and (FBB)spaces. Mathematische Zeitschrift 198,
339365 (1988)
The Projective Tensor Product of FréchetMontel Spaces.
Studia Mathematica 91, 1730 (1988).
Counterexamples to "Probléme des topologies" of Grothendieck.
Ann. Acad. Sci. Fenn. Ser. A I. Diss. 63 (1986).
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