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Uspekhi Mat. Nauk, 2003, Volume 58, Issue 1(349), Pages 33–112 (Mi umn593)  

This article is cited in 6 scientific papers (total in 7 papers)

Spectral synthesis and analytic continuation

I. F. Krasichkov-Ternovskii

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: A closed subspace of functions holomorphic in a domain of the $n$-dimensional complex space is considered. It is assumed that the subspace is invariant with respect to the partial differentiation operators and admits spectral synthesis, that is, coincides with the closure of the linear span of the common root elements in it of the partial differentiation operators. Conditions under which the elements of the invariant subspace admit analytic continuation to a larger domain are studied. The geometry of this domain depends both on the original domain and on the existence of functions admitting special lower bounds in the annihilator submodule of the invariant subspace. The same problem is also considered for topological products of invariant subspaces. The results are applied to the analytic continuation of solutions of homogeneous convolution equations.

DOI: https://doi.org/10.4213/rm593

Full text: PDF file (715 kB)
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English version:
Russian Mathematical Surveys, 2003, 58:1, 31–108

Bibliographic databases:

UDC: 517.5
MSC: Primary 32D15, 43A45; Secondary 30B40, 32F17, 46E10, 47A15, 45E10
Received: 17.07.2001

Citation: I. F. Krasichkov-Ternovskii, “Spectral synthesis and analytic continuation”, Uspekhi Mat. Nauk, 58:1(349) (2003), 33–112; Russian Math. Surveys, 58:1 (2003), 31–108

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Krivosheev A.S., “Continuation of functions from principal invariant subspaces”, Dokl. Math., 74:2 (2006), 728–730  mathnet  crossref  mathscinet  zmath  isi  elib
    2. A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz $\mathbb C^n$”, Ufimsk. matem. zhurn., 1:2 (2009), 53–74  mathnet  zmath  elib
    3. A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz $\mathbb C^n$”, Ufimsk. matem. zhurn., 1:3 (2009), 65–86  mathnet  zmath  elib
    4. A. S. Krivosheev, “Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in $\mathbb C^n$”, St. Petersburg Math. J., 22:4 (2011), 615–655  mathnet  crossref  mathscinet  zmath  isi
    5. S. G. Merzlyakov, “Integrals of exponential functions with respect to Radon measure”, Ufa Math. J., 3:2 (2011), 56–78  mathnet  zmath
    6. “Igor Fedorovich Krasichkov-Ternovskii (13.02.1935–08.03.2012)”, Ufimsk. matem. zhurn., 4:3 (2012), 187–192  mathnet
    7. V. V. Volchkov, Vit. V. Volchkov, “Spectral synthesis on the group of conformal automorphisms of the unit disc”, Sb. Math., 209:1 (2018), 1–34  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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