Infinite Products for Regularized Characteristic Function of Jacobi Operator
Result description
A function called $mathfrak{F}$ defined on a subspace of the space of complex sequences is introduced with its main algebraic properties. With the aid of $mathfrak{F}$, the characteristic function is defined for a Jacobi matrix from a certain class. Similarly as in the case of finite matrices, zeros of the characteristic function coincide with eigenvalues of the respective Jacobi operator. Further, I restrict myself on a more special subclass of investigated Jacobi matrices and derive a formula for the regularized characteristic function in terms of the infinite product of Hadamard type which forms the major part of the paper.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Infinite Products for Regularized Characteristic Function of Jacobi Operator
Original language description
A function called $mathfrak{F}$ defined on a subspace of the space of complex sequences is introduced with its main algebraic properties. With the aid of $mathfrak{F}$, the characteristic function is defined for a Jacobi matrix from a certain class. Similarly as in the case of finite matrices, zeros of the characteristic function coincide with eigenvalues of the respective Jacobi operator. Further, I restrict myself on a more special subclass of investigated Jacobi matrices and derive a formula for the regularized characteristic function in terms of the infinite product of Hadamard type which forms the major part of the paper.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Doktorandské dny 2011
ISBN
978-80-01-04907-5
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
243-252
Publisher name
Česká technika - nakladatelství ČVUT
Place of publication
Praha
Event location
Praha
Event date
Nov 11, 2011
Type of event by nationality
CST - Celostátní akce
UT code for WoS article
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Basic information
Result type
D - Article in proceedings
CEP
BA - General mathematics
Year of implementation
2011