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Complex Path Integral Representation for Semiclassical Linear Functionals

✍ Scribed by F. Marcellán; I.A. Rocha

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
491 KB
Volume
94
Category
Article
ISSN
0021-9045

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✦ Synopsis

Semiclassical linear functionals are characterized by the distributional equation D(,L)+ L=0 where , and are arbitrary polynomials with the condition deg( ) 1. Two cases are considered: (A) deg(,)>deg( ) (B) deg(,) deg( ).

In an earlier work by the authors (J. Comput. Appl. Math. 57 (1995), 239 249) integral representations are given for semiclassical functionals in case (A). Here the problem is continued and case (B) is solved: it is always possible to choose some path # in the complex plane such that every solution, regular or not, of D(,L)+ L=0 can be represented in the form (L, p) = # w(z) p(z) dz where w(z) is a solution of the differential equation (,w)$+ w=0. In some cases, the expression for L is a singular integral and a regularization process is given.

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