Sturm-Liouville operator functions

被引:0
|
作者
Fruechtl, Felix [1 ]
机构
[1] Tech Univ Munich, Zentrum Math, Boltzmannstr 3, D-85748 Garching, Germany
关键词
Sturm-Liouville operator function; cosine operator function; Bessel operator function; Legendre operator function; functional equation; Sturm-Liouville hypergroup; VALUED SOLUTIONS; COSINE FUNCTIONS; SEMIGROUPS; EQUATION; CAUCHY; PERTURBATIONS; CONVOLUTION; HYPERGROUPS; POWERS; SPACES;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Many special functions are solutions of both a differential and a functional equation. We use this duality to solve a large class of abstract Sturm-Liouville equations on the non-negative real line, initiating a theory of Sturm-Liouville operator functions; cosine, Bessel, and Legendre operator functions are special cases. We investigate properties of the generator, uniformly continuous Sturm-Liouville operator functions, give a spectral inclusion theorem, and investigate existence of an exponential norm bound. Whenever such a bound exists, we present the resolvent formula and study the relation to C-0-semigroups and C-0-groups. This general theory part is supplemented by specific examples. We show connection formulas between different types of Sturm-Liouville operator functions, determine the generator of translation operator functions on homogeneous Banach spaces, and consider Sturm-Liouville operator functions generated by multiplication operators.
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页码:5 / +
页数:49
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