Geodesic
On the number of zeros of functions in analytic quasianalytic classes
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 1, pp. 55-65 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A space of analytic functions in the unit disc with uniformly continuous derivatives is said to be quasianalytic if the boundary value of a non-zero function from the class can not have a zero of infinite multiplicity. Such classes were described in the 1950-s and 1960-s by Carleson, Rodrigues-Salinas and Korenblum. A non-zero function from a quasianalytic space of analytic functions can only have a finite number of zeros in the closed disc. Recently, Borichev, Frank, and Volberg proved an explicit estimate on the number of zeros for the case of quasianalytic Gevrey classes. Here, an estimate of similar form for general analytic quasianalytic classes is proved using a reduction to the classical quasianalyticity problem. 
@article{JMAG_2020_16_1_a3,
     author = {Sasha Sodin},
     title = {On the number of zeros of functions in analytic quasianalytic classes},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {55--65},
     year = {2020},
     volume = {16},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2020_16_1_a3/}
}
TY  - JOUR
AU  - Sasha Sodin
TI  - On the number of zeros of functions in analytic quasianalytic classes
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2020
SP  - 55
EP  - 65
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2020_16_1_a3/
LA  - en
ID  - JMAG_2020_16_1_a3
ER  - 
%0 Journal Article
%A Sasha Sodin
%T On the number of zeros of functions in analytic quasianalytic classes
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2020
%P 55-65
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2020_16_1_a3/
%G en
%F JMAG_2020_16_1_a3
Sasha Sodin. On the number of zeros of functions in analytic quasianalytic classes. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 1, pp. 55-65. http://geodesic.mathdoc.fr/item/JMAG_2020_16_1_a3/

[1] E. Bairamov, Ö. Çakar, A.M. Krall, “Non-selfadjoint difference operators and Jacobi matrices with spectral singularities”, Math. Nachr., 229 (2001), 5–14 | 3.0.CO;2-C class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[2] T. Bang, “The theory of metric spaces applied to infinitely differentiable functions”, Math. Scand., 1 (1953), 137–152 | DOI | MR | Zbl

[3] St. Petersburg Math. J., 4:2 (1993), 259–272 | MR

[4] A. Borichev, R. Frank, A. Volberg, Counting eigenvalues of Schrödinger operator with complex fast decreasing potential, arXiv: 1811.05591

[5] L. Carleson, “Sets of uniqueness for functions regular in the unit circle”, Acta Math., 87 (1952), 325–345 | DOI | MR | Zbl

[6] Math. USSR-Sb., 18:2 (1972), 181–189 | DOI | MR | Zbl

[7] Sb. Math., 196:5-6 (2005), 817–844 | DOI | DOI | MR | Zbl

[8] B.I. Korenbljum, “Quasianalytic classes of functions in a circle”, Dokl. Akad. Nauk SSSR, 164 (1965), 36–39 (Russian) | MR

[9] M. Lavie, “On disconjugacy and interpolation in the complex domain”, J. Math. Anal. Appl., 32 (1970), 246–263 | DOI | MR | Zbl

[10] S. Mandelbrojt, “Analytic functions and classes of infinitely differentiable functions”, Rice Inst. Pamphlet, 29:1 (1942), 1–142 | MR | Zbl

[11] B.S. Pavlov, “On the spectral theory of non-selfadjoint differential operators”, Dokl. Akad. Nauk SSSR, 146 (1962), 1267–1270 (Russian) | MR

[12] B.S. Pavlov, “On a non-selfadjoint Schrödinger operator”, Probl. Math. Phys., v. I, Spectral Theory and Wave Processes, Izdat. Leningrad. Univ., Leningrad, 1966, 102–132 (Russian) | MR

[13] B.C. Rennie, A.J. Dobson, “On Stirling numbers of the second kind”, J. Combinatorial Theory, 7 (1969), 116–121 | DOI | MR | Zbl

[14] B. Rodrigues-Salinas, “Funciones con momentos nulos”, Rev. Acad. Ci. Madrid, 49 (1955), 331–368 (Spanish) | MR

[15] S. Sodin, On a uniqueness theorem of E.B. Vul, arXiv: 1903.01749 | MR