Irregular boundary value problems revisited
type: Item
instance of: scholarly article
title: Irregular boundary value problems revisited
zbMATH Open document ID: 1266.34001
author: Gerhard Freiling
published in: Results in Mathematics
publication date: 2012-11-19T00:00:00Z
review text: The author gives a survey on results that have been obtained during the last century for strongly irregular boundary eigenvalue problems of the form \[ \begin{aligned} l(y)=y^{(n)}+\sum_{j=0}^{n-2}p_j(x)y^{(j)}=\lambda y, \;\;0\leq x\leq 1,\\ U_{\nu}(y)=U_{\nu 0}(y)+U_{\nu 1}(y)=0,\;\;1\leq \nu \leq n, \end{aligned} \] with complex-valued coefficients \(p_j\in L[0,1]\) and \[ U_{\nu 0}(y)=a_{\nu}y^{(k_{\nu})}(0)+\sum_{h=0}^{k_{\nu}-1}\alpha_{\nu h}y^{(h)}(0),\;\;U_{\nu 1}(y)=b_{\nu}y^{(k_{\nu})}(1)+\sum_{h=0}^{k_{\nu}-1}\beta_{\nu h}y^{(h)}(1), \] and \(a_{\nu}, b_{\nu}, \alpha_{\nu h}, \beta_{\nu h}\in \mathbb{C}\). He especially focuses on the difference concerning the convergence properties of the expansion of a given function into a series of eigenfunctions and associated functions of the above problems between the irregular case and the regular case. Also, several related results on some further classes of non-selfadjoint boundary value problems are introduced.
reviewed by: Yulian An
Mathematics Subject Classification ID: 34-02
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 6108483
zbMATH Keywords: irregular boundary value problems
zbMATH Keywords: Stone-regular boundary value problems
zbMATH Keywords: Birkhoff-regularity
MaRDI profile type: Publication
full work available at URL: s00025-012-0281-7
OpenAlex ID: W1966608982
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Irregular boundary value problems revisited (DOI)
DOI: 10.1007/S00025-012-0281-7