WEYL-TITCHMARSH THEORY FOR STURM-LIOUVILLE OPERATORS WITH DISTRIBUTIONAL POTENTIALS

被引：79

作者：

Eckhardt, Jonathan ^{[1
]}

Gesztesy, Fritz ^{[2
]}

Nichols, Roger ^{[3
]}

Teschl, Gerald ^{[1
,4
]}

机构：

[1] Univ Vienna, Fac Math, Nordbergstr 15, A-1090 Vienna, Austria

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] Univ Tennessee Chattanooga, Math Dept, Dept 6956, Chattanooga, TN 37403 USA

[4] Int Erwin Schrodinger, Inst Math Phys, A-1090 Vienna, Austria

来源：

OPUSCULA MATHEMATICA | 2013年 / 33卷 / 03期

基金：

奥地利科学基金会;

关键词：

Sturm-Liouville operators; distributional coefficients; Weyl-Titchmarsh theory; Friedrichs and Krein extensions; positivity preserving and improving semigroups;

D O I：

10.7494/OpMath.2013.33.3.467

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals (a; b) subset of R associated with rather general differential expressions of the type Tf = 1/r (-(p[f' + sf])' + sp [f ' + sf] + qf ), where the coefficients p, q, r, s are real-valued and Lebesgue measurable on (a; b), with p not equal 0, r > 0 a.e. on (a, b), and p(-1), q, r, s is an element of L-loc(1) ((a, b); d x), and f is supposed to satisfy f is an element of AC (loc) ((a, b)), p [f' + sf] is an element of AC (loc) ((a, b))

引用

页码：467 / 563

页数：97

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