50 Years with Hardy Spaces

477 Pages·11.138 MB·English

by  Anton Baranov, Sergei Kisliakov, Nikolai Nikolski

Operator Theory
Advances and Applications
261
Anton Baranov
Sergei Kisliakov
Nikolai Nikolski
Editors
50 Years
with Hardy
Spaces
A Tribute to Victor Havin

Operator Theory: Advances and Applications
Volume 261
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Anton Baranov • Sergei Kisliakov • Nikolai Nikolski
Editors
50 Years with Hardy Spaces
A Tribute to Victor Havin
Editors
Anton Baranov Sergei Kisliakov
Department of Mathematics and Mechanics Russian Academy
Saint Petersburg State University Steklov Institute of Mathematics
Saint Petersburg, Russia Saint Petersburg, Russia

Nikolai Nikolski
Université de Bordeaux
Department of Mathematics & Informatics
Talence, France

ISSN 0255-0156 ISSN2296- 4878 (electr onic)
Operator Theory: Advances and Applications
ISBN 978-3-319-59077-6 ISBN 978-3-319-59078-3 (eBook )
https://doi.org/10.1007/978-3-319-59078-3

Library of Congress Control Number: 2018935108

Mathematics Subject Classification (2010): 01-06, 26, 28, 30, 37, 41, 42, 46, 47

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Contents
Preface .................................................................. vii
Part I: Havin’s Biomathography
A.D. Baranov, S.V. Kislyakov, and N.K. Nikolski
Victor Petrovich Havin, a Life Devoted to Mathematics ............. 3
List of Publications of Victor Havin ...................................... 57
V.P. Havin
Mathematics as a Source of Certainty and Uncertainty .............. 67
K.M. Dyakonov
Remembering Victor Petrovich Havin ............................... 75
Part II: Contributed Papers
A.B. Aleksandrov
Interpolation by the Derivatives of Operator Lipschitz Functions .... 83
I. Alvarez-Romero and Yu. I. Lyubarskii
Discrete Multichannel Scattering with Step-like Potential ............ 97
A. Bondarenko and K. Seip
Note on the Resonance Method for the Riemann Zeta Function ..... 121
A. Borichev, M. Sodin and B. Weiss
Spectra of Stationary Processes on Z ................................ 141
A. Bo¨ttcher
Index Formulas for Toeplitz Operators, Approximate Identities,
and the Wolf–Havin Theorem ....................................... 159
J.E. Brennan
Bounded Point Derivations on Certain Function Algebras ........... 173
J.E. Brennan
Three Problems in Function Theory ................................. 191
vi Contents
K. Domelevo, A. Ose¸kowski and S. Petermichl
Various Sharp Estimates for Semi-discrete Riesz Transforms
of the Second Order ................................................ 229
V. Eiderman and F. Nazarov
On the Maximum Principle for the Riesz Transform ................. 257
D. Faifman, H. K¨onig and V. Milman
Submultiplicative Operators on Ck-Spaces .......................... 267
P. Ivanisvili and A. Volberg
Isoperimetric Functional Inequalities via the Maximum Principle:
The Exterior Differential Systems Approach ......................... 281
B. J¨oricke
Fundamental Groups, Slalom Curves and Extremal Length .......... 307
B. Krause and M.T. Lacey
Sparse Bounds for Random Discrete Carleson Theorems ............. 317
A. Logunov and E. Malinnikova
Nodal Sets of Laplace Eigenfunctions: Estimates of the
Hausdorff Measure in Dimensions Two and Three ................... 333
V. Maz(cid:2)ya and R. Owen
Differentiability of Solutions to the Neumann Problem with
Low-regularityData via Dynamical Systems ........................ 345
F. Nazarov and A. Olevskii
A Function with Support of Finite Measure and
“Small” Spectrum .................................................. 389
V.V. Peller
An Elementary Approach to Operator Lipschitz Type Estimates .... 395
G. Pisier
Spectral Gap Properties of the Unitary Groups: Around Rider’s
Results on Non-commutative Sidon Sets ............................. 417
I.E. Verbitsky
Sublinear Equations and Schur’s Test for Integral Operators ......... 467
OperatorTheory:
Advances andApplications,Vol.261,vii–vii
(cid:2)c SpringerInternational PublishingAG,partofSpringerNature2018
Preface
This volume is dedicated to the memory of Victor Petrovich Havin(March7,
1933–September21,2015),whosepersonality illuminated and inspired the Saint
Petersburg mathematical community(andmanyothers)duringmanydecades.
This volume contains Victor Havin’s biographical sketchwith analysis of his
influence on mathematics, the text of his address on the occasion of receiving the
Doctor Honoris Causa degree from Link¨oping University (reproduced here with
kindpermissionofthatuniversity),acompletelistofHavin’spublications,and20
articles dedicated to his memory. It should be mentioned that besides Konstantin
Dyakonov’s pure reminiscence note, the contributions by James Brennan and Al-
brecht Bo¨ttcher also contain some warm personal comments on their contacts
with V.P.
Theeditorsaredeeplyindebtedtomanyfriends,colleagues,andHavin’sfor-
merstudentsforassistanceofvariouskind,andespeciallytoEvgeniaMalinnikova
and Aleksei Poltoratskiifor accepting the task to compile mathematical commen-
tariesaboutHavin’sinfluenceoncertainfieldsofanalysis(thesecommentariesare
incorporated into V.P.’s biomathography below).
Oursincere thanks areextendedto JamesBrennan, BurglindJo¨ricke,Vladi-
mir Maz(cid:2)ya, Andrei Lodkin, and Anatolii Podkorytov for supplying us with a
number ofHavin’s photographsandgivingpermissionfor their publicationin this
volume(V.Maz(cid:2)yaalsohelpedusingettingpermissionfromLinko¨pingUniversity
toreproduceHavin’sHonorisCausaaddress).Therestofthephotographsincluded
in the volume come from Havin’s family archives (many thanks to Havin’s widow
Valentina Afanasievna) and Nikolai Nikolski’s personal archive.
We are also indebted to N. Shirokov for various help with the preparation
of the volume, to A. Podkorytovfor helping us to complete Havin’s reference list,
and to P. Mozolyako for re-typing for this edition a long quotation from a Havin
article.OurspecialthanksareextendedtoA.KhrabrovwhodidallTEXnicalwork
for the volume.
Finally, we sincerely thank the Birkh¨auser editorial staff for including the
volume in their “OT” series, and for friendly patience during the book’s prepara-
tion.
The editors
Part I
Havin’s Biomathography
OperatorTheory:
Advances andApplications,Vol.261,3–55
(cid:2)c SpringerInternational PublishingAG,partofSpringerNature2018
Victor Petrovich Havin,
A Life Devoted to Mathematics
Victor Havin (in Russian – Viktor Petroviq Havin) was one of a few charis-
maticleadersoftheSaintPetersburganalysiscommunityduringthepast50years.
Beinganoutstandingmathematician,hehasfoundedandmodelledthefaceofthe
modern Saint Petersburg analysis school,building a true hotbed of talents, which
still continues to bring forth new generations of bright scholars. Here we try to
trace his way, describe his profound impact on our community, and simply sketch
a few features of his unforgettable personality.
Below, we widely use the texts of Havin’s two interviews from “Reminis-
cencesCollections”oftheMathematicsDepartmentofSt.Petersburg(Leningrad)
University [133], [134], as well as Havin’s obituary in [Ob2016]. Here and in what
follows,referencessuchas[133]arelinkedwithHavin’sListofPublications(placed
immediatelyafterthisarticle),whereasreferencessuchas[Ob2016]arelinkedwith
this article’s own bibliography.
ThisarticleiscompiledbyA.D.Baranov,S.V.Kislyakov,andN.K.Nikolski.