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Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary conditions: II

Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary... ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 12, pp. 1668–1678.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.S. Makin, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 12, pp. 1626–1636. ORDINARY DIFFERENTIAL EQUATIONS Inverse Problems of Spectral Analysis for the Sturm–Liouville Operator with Regular Boundary Conditions: II A. S. Makin Moscow State University of Instrument Engineering and Computer Science, Moscow, Russia Received May 26, 2006 DOI: 10.1134/S0012266107120063 In the present paper, we continue the research [1] with its numbering of formulas, lemmas, and theorems. In [1], we have investigated properties of the characteristic determinant ∆( µ)of problems of types (III) and (IV). Here we prove the main result; namely, we show that the set of potentials q(x) providing an asymptotically multiple spectrum of these problems is dense in L (0,π) [and hence in L (0,π)]. For the conditions imposed in Lemma 1 on the spectrum of the Dirichlet problem not to restrict the generality of the main result, we need the following two auxiliary assertions. Lemma 2 [2]. For any function q(x) ∈ L (0,π) and any ε> 0, there exists a function q (x) ∈ 2 ε L (0,π) such that q(x) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary conditions: II

Makin, A.
Differential Equations , Volume 43 (12) – Mar 25, 2007
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266107120063
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 12, pp. 1668–1678.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.S. Makin, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 12, pp. 1626–1636. ORDINARY DIFFERENTIAL EQUATIONS Inverse Problems of Spectral Analysis for the Sturm–Liouville Operator with Regular Boundary Conditions: II A. S. Makin Moscow State University of Instrument Engineering and Computer Science, Moscow, Russia Received May 26, 2006 DOI: 10.1134/S0012266107120063 In the present paper, we continue the research [1] with its numbering of formulas, lemmas, and theorems. In [1], we have investigated properties of the characteristic determinant ∆( µ)of problems of types (III) and (IV). Here we prove the main result; namely, we show that the set of potentials q(x) providing an asymptotically multiple spectrum of these problems is dense in L (0,π) [and hence in L (0,π)]. For the conditions imposed in Lemma 1 on the spectrum of the Dirichlet problem not to restrict the generality of the main result, we need the following two auxiliary assertions. Lemma 2 [2]. For any function q(x) ∈ L (0,π) and any ε> 0, there exists a function q (x) ∈ 2 ε L (0,π) such that q(x)

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Differential Equations – Springer Journals

Published: Mar 25, 2007

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