Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011

546 Pages·2014·5.52 MB·English

by  S. Abramovich

Operator Theory
Advances and Applications
236
Manuel Cepedello Boiso
Håkan Hedenmalm
Marinus A. Kaashoek
Alfonso Montes Rodríguez
Sergei Treil
Editors
Concrete Operators,
Spectral Theory,
Operators in
Harmonic Analysis
and Approximation
22nd International Workshop in
Operator Theory and its Applications,
Sevilla, July 2011

Operator Theory: Advances and Applications
Volume 236

Founded in 1979 by Israel Gohberg

Editors:
Joseph A. Ball (Blacksburg, VA, USA)
Harry Dym (Rehovot, Israel)
Marinus A. Kaashoek (Amsterdam, The Netherlands)
Heinz Langer (Vienna, Austria)
Christiane Tretter (Bern, Switzerland)

Associate Editors: Honorary and Advisory Editorial Board:
Vadim Adamyan (Odessa, Ukraine) Lewis A. Coburn (Buffalo, NY, USA)
Wolfgang Arendt (Ulm, Germany) Ciprian Foias (College Station, TX, USA)
Albrecht Böttcher (Chemnitz, Germany) J.William Helton (San Diego, CA, USA)
B. Malcolm Brown (Cardiff, UK) Thomas Kailath (Stanford, CA, USA)
Raul Curto (Iowa, IA, USA) Peter Lancaster (Calgary, Canada)
Fritz Gesztesy (Columbia, MO, USA) Peter D. Lax (New York, NY, USA)
Pavel Kurasov (Stockholm, Sweden) Donald Sarason (Berkeley, CA, USA)
Leonid E. Lerer (Haifa, Israel) Bernd Silbermann (Chemnitz, Germany)
Vern Paulsen (Houston, TX, USA) Harold Widom (Santa Cruz, CA, USA)
Mihai Putinar (Santa Barbara, CA, USA)
Leiba Rodman (Williamsburg, VA, USA)
Ilya M. Spitkovsky (Williamsburg, VA, USA)

Subseries
Linear Operators and Linear Systems
Subseries editors:
Daniel Alpay (Beer Sheva, Israel)
Birgit Jacob (Wuppertal, Germany)
André C.M. Ran (Amsterdam, The Netherlands)

Subseries
Advances in Partial Differential Equations
Subseries editors:
Bert-Wolfgang Schulze (Potsdam, Germany)
Michael Demuth (Clausthal, Germany)
Jerome A. Goldstein (Memphis, TN, USA)
Nobuyuki Tose (Yokohama, Japan)
Ingo Witt (Göttingen, Germany)
Manuel Cepedello Boiso
Håkan Hedenmalm
Marinus A. Kaashoek
Alfonso Montes Rodríguez
Sergei Treil
Editors
Concrete Operators,
Spectral Theory, Operators
in Harmonic Analysis
and Approximation
22nd International Workshop in Operator Theory
and its Applications, Sevilla, July 2011
Editors
Manuel Cepedello Boiso Håkan Hedenmalm
Departamento de Análisis Matemático Department of Mathematics
Universidad de Sevilla The Royal Institute of Technology
Sevilla Stockholm
Spain Sweden
Marinus A. Kaashoek Alfonso Montes Rodríguez
Dept. of Mathematics & Computer Science Departamento de Análisis Matemático
Free University Amsterdam Universidad de Sevilla
Amsterdam Sevilla
The Netherlands Spain
Sergei Treil
Department of Mathematics
Brown University
Providence, RI
USA
ISSN 0255-0156 ISSN 2296-4878 (electronic)
ISBN 978-3-0348-0647-3 ISBN 978-3-0348-0648-0 (eBook)
DOI 10.1007/978-3-0348-0648-0
Springer Basel Heidelberg New York Dordrecht London
Mathematics Subject Classification (2010): 47-06; 34B45, 47A10, 47B38, 93D15

© Springer Basel 2014
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Contents
Israel Gohberg Memorial Session ......................................... ix
L. Rodman
Research Work of Israel Gohberg .................................... xvii
S. Abramovich and L.-E. Persson
Some New Refined Hardy Type Inequalities
with Breaking Points 𝑝=2 or 𝑝=3 ................................. 1
Yu. Arlinski˘ı and S. Belyi
Non-negative Self-adjoint Extensions in Rigged Hilbert Space ....... 11
A. Barreras and J.M. Pen˜a
Matrices with Bidiagonal Decomposition, Accurate
Computations and Corner Cutting Algorithms ...................... 43
A. Barton and S. Mayboroda
Boundary-value Problems for Higher-order Elliptic Equations
in Non-smooth Domains ............................................ 53
M. Bendaoud and M. Sarih
Additive Maps Preserving the Inner Local Spectral Radius .......... 95
L.F. Campos, A.B. Lebre and J.S. Rodr´ıguez
On some Generalized Riemann Boundary Value Problems
with Shift on the Real Line ......................................... 103
G. Cassier and J. Verliat
Generalized Extremal Vectors and Some New Properties ............ 117
F. Colonna and M. Tjani
Weighted Composition Operators from the Analytic
Besov Spaces to BMOA ............................................. 133
R.G. Douglas and K. Wang
Some Remarks on Essentially Normal Submodules .................. 159
S.R. Garcia and C. Hammond
Which Weighted Composition Operators are
Complex Symmetric? ............................................... 171
vi Contents
S.R. Garcia, W.T. Ross and W.R. Wogen
𝐶∗-algebras Generated by Truncated Toeplitz Operators ............ 181
S. Gefter and T. Stulova
On Some Vector Differential Operators of Infinite Order ............. 193
J.F. Glazebrook
Wiener–Hopf Type Operators and Their Generalized
Determinants ....................................................... 205
M. Gonz´alez
Tauberian Operators. Properties, Applications and
Open Problems ..................................................... 231
H. Guediri
Products of Toeplitz and Hankel Operators on the Hardy Space
of the Unit Sphere .................................................. 243
M. Harju and V. Serov
Three-dimensional Direct and Inverse Scattering for the
Schro¨dinger Equation with a General Nonlinearity .................. 257
A.Yu. Karlovich and I.M. Spitkovsky
The Cauchy Singular Integral Operator on Weighted Variable
Lebesgue Spaces .................................................... 275
B.A. Kats
Extension of Certain Distributions on Weighted Ho¨lder
Space and the Riemann Boundary Value Problem for
Non-rectifiable Curves .............................................. 293
G. Krishna Kumar and S.H. Kulkarni
An Analogue of the Spectral Mapping Theorem for
Condition Spectrum ................................................ 299
M. Loaiza and A. S´anchez-Nungaray
Commutative Algebras of Toeplitz Operators on the Super Upper
Half-plane: Quasi-hyperbolic and Quasi-parabolic Cases ............. 317
F. Martin and E. Wegert
Computing the Hilbert Transform in Wavelet Bases on
Adaptive Grids ..................................................... 337
K. Matsuoka
𝐵 -Campanato Estimates for Commutators of
𝜎
Caldero´n–ZygmundOperators ...................................... 357
Y. Abu Muhanna and E.-B. Yallaoui
Composition Operators on Large Fractional Cauchy
Transform Spaces ................................................... 371
Contents vii
A. Per¨al¨a, A. Schuster and J.A. Virtanen
Hankel Operators on Fock Spaces ................................... 377
R. Picard and B.A. Watson
Evolutionary Problems Involving Sturm–Liouville Operators ........ 391
S.C. Power
Crystal Frameworks, Matrix-valued Functions
and Rigidity Operators ............................................. 405
E. Rela
Refined Size Estimates for Furstenberg Sets via Hausdorff Measures:
A Survey of Some Recent Results ................................... 421
A. Sahmurova and V.B. Shakhmurov
Singular Degenerate Problems Occurring in Atmospheric
Dispersion of Pollutants ............................................. 455
A. Sergeev
Harmonic Spheres Conjecture ....................................... 463
D.T. Stoeva and P. Balazs
Riesz Bases Multipliers ............................................. 475
A. Torokhti
Operator Approximation for Processing of Large Random
Data Sets ........................................................... 483
A.A. Vladimirov and I.A. Sheipak
On Spectral Periodicity for the Sturm–Liouville Problem:
Cantor Type Weight, Neumann and Third Type Boundary
Conditions .......................................................... 509
V.V. Vlasov and N.A. Rautian
Spectral Analysis and Representations of Solutions of Abstract
Integro-differential Equations in Hilbert Space ...................... 517

OperatorTheory:
Advances andApplications,Vol.236,ix–xvi
⃝c 2014SpringerBasel
Israel Gohberg Memorial Session
This text is composed by the Editors from the speeches given at the Memorial
Session preceding the Conference Dinner.
Opening
Rien Kaashoek (VU University, Amsterdam)
Ladies and gentlemen, dear friends and colleagues.
Israel Gohberg passed away on October 12, 2009. I welcome you at this special
sessiondedicated to his memory. I am speaking on behalf of the IWOTA Steering
Committee. IWOTA stands for International Workshop on Operator Theory and
its Applications. As many of you know, professor Israel Gohberg was the first
and only president of the Steering Committee. Together with William Helton he
initiated in 1974 the IWOTA idea and as president he determined from the very
beginning until the end of his life the general principles and the main directions
of the IWOTA meetings.
I am very grateful to Alfonso Rodrigues, the chief organizer of the present
IWOTA, fordedicating the conferencetothe memoryofIsraelGohbergandorga-
nizing this special session. On the web site of the conference the following words
were used: Being one of the main promoters of the IWOTA series Gohberg’s kind
courageous humor will not be forgotten.
Thisevening,justbeforetheconferencebanquet,wehavethisspecialsession
to commemorate Gohberg’s great mathematical legacy, his outstanding work and
his wonderful personality. We do that in the presence of his wife Bella Gohberg,
who also will contribute to this session, his sister Feija, and his two daughters
Zvia and Yanina. I am very happy that they are here. I hope that they will expe-
riencethe greatinfluence their husband,brotherandfather,hadonus, his former
colleagues, students, co-workers,friends, and on the field we are working in.
Thesessionbeginswithamathematicalorientedcontribution,ashortreview
of Israel Gohberg’s research work by Leiba Rodman, the first Ph.D. student of
Gohberg after his emigration in 1974 from Kishinev, Moldavia to Israel. Next the
programconsists ofpersonal reminiscences onIsrael Gohbergby Nikolai Nikolski,
a colleague fromthe very beginning, Yuli Eidelman, who was his co-workerin the
field of numerical analysis, and Henri Landau, a life long friend of Gohberg and
theGohbergfamily.ThesessionwillbeconcludedbyMrs.BellaGohbergwhowill