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Scientific Publishing Center
Document Details
Document Type
:
Article In Journal
Document Title
:
Product Formula for Imaginary Resolvents and its Application
قاعدة حاصل الضرب للمؤثرات الحلية التخيلية وتطبيقها
Subject
:
mathematics
Document Language
:
English
Abstract
:
ABSTRACT. In this paper we study a product fonnula for imagin~ resolvents of the Schrodinger operator -~ + q as well as elliptic differential operators (generalized Schrodinger operators) of a complex Hilbert space H under the conditions [q], [ak] and [bk]. The resolvents and related functions are given by an integral kernel, which is bounded by a convolution with a radial decreasing L\- function. We examine the weakest conditions under which the Schrodingerequation i ~ = Ku , with u(x,O) = v(x) , V E D(K) and K the realization in H of the Schrodinger operator. (a,ndthe generalized SchrOdinger operator), can be solved. The solutionis represented as a sequential limit of finite dimensional integrals involving the kerne[ of the imaginary resolvent of (-~) and ( I akDk).
ISSN
:
1012-1319
Journal Name
:
Science Journal
Volume
:
1
Issue Number
:
1
Publishing Year
:
1409 AH
1989 AD
Number Of Pages
:
9
Article Type
:
Article
Added Date
:
Sunday, October 11, 2009
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
محمود صبري سيف
MAHMOUD SABRY SAIF
Researcher
Files
File Name
Type
Description
22671.pdf
pdf
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