The convergence of Fourier series in eigenfunctions of the Schrodinger operator with Kato potential

被引：3

作者：

Serov, VS ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 117234, Russia

来源：

MATHEMATICAL NOTES | 2000年 / 67卷 / 5-6期

关键词：

Schrodinger operator; eigenfunction expansion; generalized Fourier series; convergence;

D O I：

10.1007/BF02676337

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain sharp conditions for the absolute uniform convergence of Fourier series in the eigenfunctions of the Schrodinger operator with Kato potential in a bounded domain for functions lying in the domains of generalized fractional powers of the original Schrodinger operator or in generalized Besov classes with a sharp exponent.

引用

页码：639 / 645

页数：7

共 15 条

[1]

ALIMOV SA, 1985, ACTA SCI MATH, V48, P5

[2]

ALIMOV SA, 1983, ACTA SCI MATH, V45, P5

[3]

ASHUROV RR, 1987, DIFF URAVN, V23, P169

[4]

CYCON H. L, 1987, Schrodinger operators with application to quantum mechanics and global geometry

[5]

ILIN VA, 1991, SPECTRAL THEORY DIFF

[6] SCHRODINGER OPERATORS WITH SINGULAR POTENTIALS [J].

KATO, T .

ISRAEL JOURNAL OF MATHEMATICS, 1972, 13 (1-2) :135-148

[7]

KHALMUKHAMEDOV AR, 1984, DIFF URAVN, V20, P1642

[8]

KHALMUKHAMEDOV AR, 1986, DIFF URAVN, V22, P2107

[9]

Reed M., 1975, Fourier Analysis, Self-Adjointness

[10]

RICSZ F, 1965, LECONS ANAL FONCTION

← 1 2 →