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

被引：76
|
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))
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页码：467 / 563
页数：97
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