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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 3, Pages 317–347 (Mi msb2024)  

This article is cited in 18 scientific papers (total in 18 papers)

Theorems of Tauberian type on the distribution of zeros of holomorphic functions

A. A. Shkalikov


Abstract: Let $f(\lambda)$ and $g(\lambda)$ be holomorphic functions of finite order in a sector $\Lambda$, and let $n(f,r)$ and $n(g,r)$ be the distribution functions of their zeros inside this sector. Theorems established in this article permit the assertion that $n(f,r)$ and $n(g,r)$ are equivalent if $f(\lambda)$ and $g(\lambda)$ differ “little” on the boundary of $\Lambda$. In the second part of the article domains bounded by curves of parabola type are considered instead of a sector $\Lambda$, and theorems are established which generalize and strengthen Tauberian theorems with a remainder for the distributions of zeros of entire functions and for Stieltjes transforms.
Bibliography: 28 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:2, 315–344

Bibliographic databases:

UDC: 517.53
MSC: Primary 30C15, 40E05; Secondary 26A42, 30D15, 30D50
Received: 08.06.1982

Citation: A. A. Shkalikov, “Theorems of Tauberian type on the distribution of zeros of holomorphic functions”, Mat. Sb. (N.S.), 123(165):3 (1984), 317–347; Math. USSR-Sb., 51:2 (1985), 315–344

Citation in format AMSBIB
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\by A.~A.~Shkalikov
\paper Theorems of Tauberian type on the distribution of zeros of holomorphic functions
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 3
\pages 317--347
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=735710}
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\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 2
\pages 315--344
\crossref{https://doi.org/10.1070/SM1985v051n02ABEH002862}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tsihistavi Z., “On Spectral Asymptotics for Eigenvalue Problem Depending Non-Linearly on Parameter”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1989, no. 2, 84–86  isi
    2. K. Kh. Boimatov, A. G. Kostyuchenko, “Spectral asymptotics of nonselfadjoint elliptic systems of differential operators on bounded domains”, Math. USSR-Sb., 71:2 (1992), 517–531  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. K. Kh. Boimatov, A. G. Kostyuchenko, “Spectral asymptotics of polynomial pencils of differential operators on a compact manifold without boundary”, Funct. Anal. Appl., 24:2 (1990), 146–148  mathnet  crossref  mathscinet  zmath  isi
    4. Boimatov K., “On Eigenvalue Asymptotics of Non-Self-Adjoint Elliptic-Systems in Arbitrary Domain with Finite Measure”, 315, no. 6, 1990, 1289–1293  mathscinet  isi
    5. Boimatov K., Kostiuchenko A., “Spectral Asymptotics for Polynomial Bundles of Differential-Operators”, 313, no. 5, 1990, 1036–1040  mathscinet  isi
    6. K. Kh. Boimatov, “The spectral asymptotics of pseudodifferential systems elliptic in the sense of Douglis and Nirenberg”, Russian Math. Surveys, 46:5 (1991), 183–184  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Boimatov K., “Spectral Asymptotics of Non-Self-Conjugate Pseudodifferential-Operators in Bounded Domains”, 317, no. 3, 1991, 530–534  mathscinet  isi
    8. K. Kh. Boimatov, A. G. Kostyuchenko, “Spectral asymptotics of polynomial pencils of differential operators in bounded domains”, Funct. Anal. Appl., 25:1 (1991), 5–16  mathnet  crossref  mathscinet  zmath  isi
    9. Boimatov K., “Spectral Asymptotics of Linear and Nonlinear Pencils of Douglis-Nirenberg Elliptic Pseudodifferential-Operators”, 322, no. 3, 1992, 441–445  mathscinet  isi
    10. Boimatov K., “Spectral Asymptotic of Nonself-Adjoint Degenerate Elliptic-Systems of Differential-Operators”, Dokl. Akad. Nauk, 330:5 (1993), 533–538  mathnet  mathscinet  isi
    11. Boimatov K., “Some Asymptotical Formulas for the Elliptic Operations in R(N), That Are Far From Selfadjointness”, Dokl. Akad. Nauk, 344:6 (1995), 730–735  mathnet  mathscinet  zmath  isi
    12. A. Sameripour, K. Seddighi, “Distribution of eigenvalues of nonself-adjoint elliptic systems degenerate on the domain boundary”, Math. Notes, 61:3 (1997), 379–384  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. S. N. Tumanov, A. A. Shkalikov, “On the Spectrum Localization of the Orr–Sommerfeld Problem for Large Reynolds Numbers”, Math. Notes, 72:4 (2002), 519–526  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. A. A. Shkalikov, “Spectral Portraits of the Orr–Sommerfeld Operator with Large Reynolds Numbers”, Journal of Mathematical Sciences, 124:6 (2004), 5417–5441  mathnet  crossref  mathscinet  zmath
    15. A. A. Lesnykh, “Estimates of the Solutions of Difference-Differential Equations of Neutral Type”, Math. Notes, 81:4 (2007), 503–517  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. A. A. Shkalikov, “On the basis property of root vectors of a perturbed self-adjoint operator”, Proc. Steklov Inst. Math., 269 (2010), 284–298  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    17. A. A. Shkalikov, “Perturbations of self-adjoint and normal operators with discrete spectrum”, Russian Math. Surveys, 71:5 (2016), 907–964  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. L. G. Valiullina, Kh. K. Ishkin, R. I. Marvanov, “Spectral asymptotics for fourth order differential operator with two turning points”, Ufa Math. J., 10:4 (2018), 24–39  mathnet  crossref  isi
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