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Mat. Zametki, 2015, Volume 97, Issue 2, Pages 249–254 (Mi mz10437)  

This article is cited in 1 scientific paper (total in 1 paper)

An Example in the Theory of Bisectorial Operators

A. V. Pechkurov

Voronezh State University

Abstract: An unbounded operator is said to be bisectorial if its spectrum is contained in two sectors lying, respectively, in the left and right half-planes and the resolvent decreases at infinity as $1/\lambda$. It is known that, for any bounded function $f$, the equation $u'-Au=f$ with bisectorial operator $A$ has a unique bounded solution $u$, which is the convolution of $f$ with the Green function. An example of a bisectorial operator generating a Green function unbounded at zero is given.

Keywords: bisectorial operator, linear differential equation, Green function, resolvent set, Fourier series.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00378
14-01-31196
This work was supported by the Russian Foundation for Basic Research (grants no. 13-01-00378 and no. 14-01-31196).


DOI: https://doi.org/10.4213/mzm10437

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English version:
Mathematical Notes, 2015, 97:2, 243–248

Bibliographic databases:

UDC: 517.986
Received: 14.11.2013
Revised: 23.06.2014

Citation: A. V. Pechkurov, “An Example in the Theory of Bisectorial Operators”, Mat. Zametki, 97:2 (2015), 249–254; Math. Notes, 97:2 (2015), 243–248

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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. V. G. Kurbatov, I. V. Kurbatova, “Computation of Green's function of the bounded solutions problem”, Comput. Methods Appl. Math., 18:4 (2018), 673–685  crossref  mathscinet  isi  scopus
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