Transmutations for Strings

Transmutations for Strings

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We investigate the existence and representation of transmutations, also known as transformation operators, for strings. Using measure theory and functional analytic methods we prove their existence and study their representation. We show that in general they are not close to unity since their repre...

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Main Authors: Amin Boumenir, Vu Kim Tuan
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2008-07-01
Series:Armenian Journal of Mathematics
Online Access:http://armjmath.sci.am/index.php/ajm/article/view/9
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spelling doaj-3b8f23fd8ac3433ba9fa64a0357053542020-11-24T21:32:39ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632008-07-0111Transmutations for StringsAmin Boumenir0Vu Kim Tuan1Department of Mathematics University of West Georgia Carrollton, GA30118, USADepartment of Mathematics University of West Georgia Carrollton, GA30118, USA We investigate the existence and representation of transmutations, also known as transformation operators, for strings. Using measure theory and functional analytic methods we prove their existence and study their representation. We show that in general they are not close to unity since their representation does not involve a Volterra operator but rather the eigenvalue parameter. We also obtain conditions under which the transmutation is either a bounded or a compact operator. Explicit examples show that they cannot be reduced to Volterra type operators.   http://armjmath.sci.am/index.php/ajm/article/view/9
collection DOAJ
language English
format Article
sources DOAJ
author Amin Boumenir
Vu Kim Tuan
spellingShingle Amin Boumenir
Vu Kim Tuan
Transmutations for Strings
Armenian Journal of Mathematics
author_facet Amin Boumenir
Vu Kim Tuan
author_sort Amin Boumenir
title Transmutations for Strings
title_short Transmutations for Strings
title_full Transmutations for Strings
title_fullStr Transmutations for Strings
title_full_unstemmed Transmutations for Strings
title_sort transmutations for strings
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2008-07-01
description We investigate the existence and representation of transmutations, also known as transformation operators, for strings. Using measure theory and functional analytic methods we prove their existence and study their representation. We show that in general they are not close to unity since their representation does not involve a Volterra operator but rather the eigenvalue parameter. We also obtain conditions under which the transmutation is either a bounded or a compact operator. Explicit examples show that they cannot be reduced to Volterra type operators.  
url http://armjmath.sci.am/index.php/ajm/article/view/9
work_keys_str_mv AT aminboumenir transmutationsforstrings
AT vukimtuan transmutationsforstrings
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