An estimate for the residual term in asymptotic formulas for the spectral function of the Sturm-Liouville operator
Journal Article
·
· Journal of Mathematical Sciences
We consider the Sturm-Liouville boundary-value problem -y{double_prime} + q(x) y = {mu} y; y{prime} (0) = 0; 0 {le} x < {infinity}, where the potential q(x) is real and locally summable, and we use c({lambda}, x) to denote the solution to the equation -y{double_prime} + q(x)y = {lambda} {sup 2}y with initial data c({lambda}, 0) = 1, c{prime} ({lambda}, 0) = 1, c{prime}({lambda}, 0) = 0. According to Weyl`s theorem, there exists at least one nondecreasing spectral function {rho}({mu}) (-{infinity} < {mu} < {infinity}) for this problem that generates the expansion formulas.
- OSTI ID:
- 161614
- Journal Information:
- Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 4 Vol. 76; ISSN 1072-1964; ISSN JMTSEW
- Country of Publication:
- United States
- Language:
- English
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