zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point. (English) Zbl 1012.34083
The authors study the inverse spectral problem for the Sturm-Liouville equation $$ -y''+q(x)y = \lambda y, \quad x\in (0,a)\cup (a,\infty),$$ with a jump condition in an interior point $x=a: (y,y')^t(a+0) = A(y, y')^t(a-0)$ and the boundary condition $y'(0)=hy(0)$. The potential $q(x)$ is assumed to be a complex-valued function vanishing at infinity such that $(1+x)q(x)\in L_1(0, \infty)$. The authors introduce appropriate spectral data (an analogue of the Weyl function), prove a uniqueness theorem and give a reconstruction procedure based on an integral equation obtained by the contour integration method.

34L40Particular ordinary differential operators
34A55Inverse problems of ODE
47E05Ordinary differential operators
34B20Weyl theory and its generalizations
34B24Sturm-Liouville theory
Full Text: DOI