Alexander Borichev
Welcome
to my home page
Here is the list of my
publications
1. Convolution equations in spaces of
sequences with exponential
restrictions on growth,Zapiski Nauchnyh Seminarov LOMI 149 (1986), 107-115, 188-189;
English translation in J. Soviet Math. 42 (1988), no. 2, 1614-1620, MR 88f:42026.
2. Boundary uniqueness theorems for almost analytic functions and asymmetric algebras
of sequences, Matemat. Sbornik 136 (1988), no. 3, 324-340; English translation in
Math.
3. (with A.L.Volberg) Convolution Uniqueness theorems for almost analytic functions,
Algebra i Analiz 1 (1989), 146-177; English translation in Leningrad Mathematical Journal
1 (1990), no. 1, 157-191, MR 90k:30090.
4. Convolution equations and the structure of 1- and 2-invariant subspaces in the scale
of spaces of rough growth, Doklady Akad. Nauk USSR 304 (1989), no. 4, 788-792;
English translation in Soviet Math. Dokl. 39 (1989), no. 1, 140-144, MR 90d:46063.
5. A Titchmarsh-type convolution theorem on the group Z, Arkiv för Matematik 27 (1989),
no. 2, 179-187, MR 90m:42019.
6. The generalized Fourier transformation, Titchmarsh's theorem and asymptotically
holomorphic functions, Algebra i Analiz 1 (1989), no. 4, 17-53; English translation in
Leningrad Mathematical Journal 1 (1990), 825-857, MR 91m:42011.
7. Completeness of systems of translates and uniqueness theorems for asymptotically
holomorphic functions, Progress in Approximation Theory (eds. A.A.Gonchar, E.B.Saff),
Springer-Verlag (1992), 285-293.
8. Analytical quasianalyticity and asymptotically holomorphic functions, Algebra i Analiz 4
(1992), no. 2, 70-87; English translation in St.-Petersburg Mathematical Journal 4 (1993),
no. 2, 259-272, MR 93h:30055.
9. (with H.Hedenmalm) Approximation in a class of Banach algebras of quasianalytically
smooth analytic functions, J. of Functional Analysis 114 (1993), 359-390, MR 95a:46075.
10. (with H.Hedenmalm) Completeness of translates in weighted spaces on the half-line,
Acta Mathematica 174 (1995), no.1, 1-84, MR 96f:43003. Click to download ps file.
11. (with H.Hedenmalm) Cyclicity in Bergman-type spaces, International Mathematics
Research Notices (1995), no.5, 253-262, MR 96h:46030.
12. (with A.L.Volberg) Finiteness of limit cycles and uniqueness for asymptotically
holomorphic functions, Algebra i Analiz 7 (1995), no.3, 43-75; English translation in
St.-Petersburg Mathematical Journal 7 (1996), no.3, 343-368, MR 96h:34045.
Click to download ps file.
13. (with H.Aikawa) Quasiadditivity and measure property of capacity and the tangential
boundary behavior of harmonic functions, Potential Theory - ICPT 94 (eds. Král,
Lukes, Netuka, Veselý) (1996), 219-227, MR 97e:31002. Click to download ps file.
14. Beurling algebras and the generalized Fourier transform, Proceedings of the London
Mathematical Society (3) 73 (1996), 431-480, MR 97k:46063. Click to download ps file.
15. Estimates from below and cyclicity in Bergman-type spaces, International Mathematics
Research Notices (1996), no.12, 603-611, MR 97f:46040. Click to download ps file.
16. (with H.Aikawa) Quasiadditivity and measure property of capacity and the tangential
boundary behavior of harmonic functions, Transactions of the American Mathematical
Society 348 (1996), 1013-1030, MR 96h:31004. Click to download ps file.
17. (with H.Hedenmalm) Harmonic functions of maximal growth: invertibility and cyclicity in
Bergman spaces, Journal of the American Mathematical Society 10 (1997), no. 4,
761-796, MR 98a:30066. Click to download ps file.
18. (with M.Sodin) Density of polynomials and the Hamburger moment problem, C. R. Acad.
Sci. Paris 327 (1998), 11-16, MR 99e:41016. Click to download ps file.
19. The polynomial approximation property in Fock-type spaces, Mathematica Scandinavica
82 (1998), 256-264, MR 2000i:46020. Click to download ps file.
20. Invariant subspaces of given index in Banach spaces of analytic functions, Journal für die
reine und angewandte Mathematik 505 (1998), 23-44, MR 2000i:47010. Click to download ps file.
21. (with M.Sodin) The Hamburger moment problem and weighted polynomial approximation
on discrete subsets of the real line, Journal d'Analyse Math. 76 (1998), 219-264, MR
2000g:44017. Click to download ps file.
22. (with M.Sodin) Weighted polynomial approximation and the Hamburger moment problem,
Complex Analysis and Differential Equations. Proceedings of the Marcus Wallenberg
Symposium in Honor of Matts Essén Held in
Kiselman, Vretblad).
23. On weighted polynomial approximation with monotonic weights, Proceedings of
the American Mathematical Society 128 (2000), 3613-3619, MR 2001b:41003. Click to download ps file.
24. (with M.Sodin) Krein's entire functions and the Bernstein approximation problem, Illinois
Journal of Mathematics 45 (2001), 167-185, MR 2002d:30031. Click to download ps file.
25. (with I.Kleschevich) An access theorem for continuous functions, Journal of the London
Mathematical Society 64 (2001), 81-92, MR 2002c:26019. Click to download ps file.
26. On the closure of polynomials in weighted spaces of functions on the real line, Indiana
University Mathematical Journal 50 (2001), 829-846, MR 2003f:41005. Click to download ps file.
27. (with R.Deville and E.Matheron) Strongly sequentially continuous functions, Quaestiones
Mathematicae 24 (2001), 535-548, MR 2002k:46027. Click to download ps file.
28. (with E.Abakumov) Shift invariant subspaces with arbitrary indices in lp spaces,
Journal of Functional Analysis 188 (2002), 1-26, MR 2003b:47014. Click to download ps file.
29. Convolution equations with restrictions on supports, Algebra i Analiz 14 (2002), no. 2,
1-10; St.-Petersburg Mathematical Journal 14 (2003), no. 2, 179-187, MR 2003i:47031.
Click to download ps file.
30. On the minimum of harmonic functions, Journal d'Analyse Mathematique 89 (2003),
199-212, MR 2004h:31001. Click to download ps file.
31. (with H.Hedenmalm and A.Volberg) Large Bergman spaces: invertibility, cyclicity, and
subspaces of arbitrary index, Journal of Functional Analysis 207 (2004), 111-160, MR 2005d:30052;
see also preprint math.FA/0304318
32. On the Bekolle-Bonami condition, Mathematische Annalen 328 (2004), 389-398,
MR 2005c:30040. Click to download ps file.
141 (2004), 277-284, MR 2005a:37072; see also preprint math.DS/0304199
34. (with F.Nazarov and M.Sodin) Lower bounds for quasianalytic functions, II. The Bernstein
quasianalytic functions, Mathematica Scandinavica 95 (2004), 44-58, MR 2005k:30071;
see also preprint math.CA/0301217
35. Distortion growth for iterations of diffeomorphisms of the interval, Geometric and Functional Analysis
14 (2004), 941-964, MR 2005h:37084; see also preprint math.DS/0304440
36. (with Yu.Lyubarskii) Uniqueness theorems for Korenblum type spaces,
Mini-Workshop: Operators on Spaces of Analytic Functions, Oberwolfach report 36/2005, 2059-2061,
see http://www.mfo.de/cgi-bin/path?cgi-bin/tagungsdb?type=21&tnr=0533a
37. (with A.Nicolau and P.Thomas) Harmonic and superharmonic majorants on the disk,
Bulletin of the London Mathematical Society 38 (2006), no.2, 250-260; see also preprint math.CV/0304482
Here are some recent preprints
38. (with R.Dhuez and K.Kellay) Sampling and interpolation in radial weighted spaces of analytic
functions, see preprint math.CV/0506297
39. (with Yu.Lyubarskii) Uniqueness theorems for Korenblum type spaces, see preprint math.CV/0512425
40. (with R.Chill and Yu.Tomilov) Uniqueness theorems for (sub-)harmonic functions with applications
to operator theory, see preprint math.CV/0512460
41. (with A.D.Baranov and V.P.Havin) Majorants of meromorphic functions with fixed poles, 32 pp.,
see preprint math.CV/0605052
Conference
proceedings
42. (Editors Alexander A. Borichev
and Nikolai K. Nikolski)
Systems, Approximation, Singular Integral Operators, and Related
Topics,
Proceedings of IWOTA 2000, Operator Theory: Advances and Applications,
129,
Birkhauser Verlag,
2001,
xv+527 pp, ISBN 3-7643-6645-1, MR
2002k:00031.
43. (Editors Alexander Borichev, Hakan Hedenmalm and Kehe Zhu)
Bergman Spaces and Related Topics in Complex Analysis,
Proceedings of a Conference in Honor of Boris Korenblum's 80th Birthday,
to appear in AMS, 2006, xxi+205 pp.
Organization of conferences
13-16.06.2000 International Conference in Operator Theory and its Applications, IWOTA--2000, Bordeaux, France.
30.09-4.10.2002 Spaces of Analytic Functions and their Operators, CIRM, Marseille, France.
16-17.05.2005 Journées d'Analyse Harmonique, Bordeaux, France.
5-9.06.2006 Spaces of Analytic Functions and their Operators, CIRM, Marseille, France.