Green's function and Carleman's formula for transmission problems
type: Item
instance of: scholarly article
title: Green's function and Carleman's formula for transmission problems
author: Kadriye Aydemir
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2022-10-31T00:00:00Z
review text: The author deals with the problem \begin{gather*} -p(x)u''+q(x)u=\lambda u(x),\quad x\in[-1,0)\cup(0,1],\\ (\ln y)'(-1)=a_1, \quad (\ln y)'(1)=a_2,\\ y(0^+)-y(0^-)=b_1u(0^-),\quad y'(0^+)-y'(0^-)=b_2u'(0^-), \end{gather*} where \[ p(x)=\begin{cases} p_1>0 &\text{for } x\in[-1,0) \\ p_2>0 &\text{for } x\in(0,1], \end{cases} \] \(q\) is real-valued continuous function on \([-1,0)\) and \((0,1]\), \(a_1,a_2,b_1,b_2\) are real constants and \(\lambda\) is a spectral parameter so that \(a_1\neq 0\), \(a_2\neq 0\), \(b_1>-1\), \(b_2>-1\). In particular, the author constructs the Green's function of the problem and introduces a series expansion of eigenfunctions, Parseval's equality and Carleman's formula.
reviewed by: Ekin Ugurlu
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 34L10
zbMATH DE Number: 7610171
zbMATH Keywords: Sturm-Liouville problems
zbMATH Keywords: transmission conditions
zbMATH Keywords: Green's function
zbMATH Keywords: Parseval equality
zbMATH Keywords: Carleman equation
MaRDI profile type: Publication
full work available at URL: s40840-022-01379-w
OpenAlex ID: W4294405797
Wikidata QID: Q113891471
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DOI: 10.1007/S40840-022-01379-W
description: scientific article; zbMATH DE number 7610171