On characteristic matrices and eigenfunction expansions of two singular point symmetric systems

We study general (not necessarily Hamiltonian) first‐order symmetric systems Jy′−B(t)y=Δ(t)f(t) on an interval I=(a,b) with both singular endpoints a and b. For such a system we give a criterion of existence and description of self‐adjoint separated boundary conditions. We prove the Titchmarsh type...

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Bibliographic Details
Published in:Mathematische Nachrichten Vol. 288; no. 2-3; pp. 249 - 280
Main Author: Mogilevskii, Vadim
Format: Journal Article
Language:English
Published: Weinheim Blackwell Publishing Ltd 01.02.2015
Wiley Subscription Services, Inc
Subjects:
34B20
34B40
34L10
47A06
47B25
Boundary conditions
characteristic matrix
Finite element analysis
First-order symmetric system
Fourier transform
m-function
self-adjoint separated boundary conditions
spectral function of a boundary problem
ISSN:0025-584X, 1522-2616
Online Access:Get full text
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Summary:We study general (not necessarily Hamiltonian) first‐order symmetric systems Jy′−B(t)y=Δ(t)f(t) on an interval I=(a,b) with both singular endpoints a and b. For such a system we give a criterion of existence and description of self‐adjoint separated boundary conditions. We prove the Titchmarsh type formula for the characteristic matrix Ω(λ) of the self‐adjoint linear relation in LΔ2(I) generated by separated boundary conditions as well as by a certain type of mixed boundary conditions. This formula enables one to express Ω(λ) in terms of the m‐functions at the endpoints of I. By using the Titchmarsh type formula we parametrize all spectral functions corresponding to boundary problems with the mentioned boundary conditions immediately in terms of self‐adjoint boundary parameters at the end points a and b.
Bibliography:istex:1D6F68BDC34828EE525B8C0223721C81218B797E
ark:/67375/WNG-SBLHPNST-F
ArticleID:MANA201300242
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201300242