Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Volkovaya V. A. Synthesis in the Polynomial Kernel of Two Analytic Functionals. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 251-262. DOI: 10.18500/1816-9791-2014-14-3-251-262, EDN: SMSJTN

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.09.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.5
DOI: 
10.18500/1816-9791-2014-14-3-251-262
EDN: 
SMSJTN

Synthesis in the Polynomial Kernel of Two Analytic Functionals

Autors: 
Volkovaya Victoria Anatolievna, Kuban State University
Abstract: 

Let ¼ be an entire function of minimal type and order ½ = 1 and let ¼(D) be the corresponding differential operator. Maximal ¼(D)-invariant subspace of the kernel of an analytic functional is called its C[¼]-kernel. C[¼]-kernel of a system of analytic functionals is called the intersection of theirC[¼]-kernels. The paper describes the conditions which allow synthesis ofC[¼]-kernels of two analytical functionals with respect to the root elements of the differential operator ¼(D). 

Key words: 
spectral synthesis
differential operator of infinite order
invariant subspaces
submodules of entire functions
References: 
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Received: 
16.03.2014
Accepted: 
17.07.2014
Published: 
10.09.2014
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