ISSN:
1572-9036
Keywords:
33A45
;
34A55
;
34B25
;
35A22
;
35P10
;
35P25
;
35R30
;
42A38
;
42A85
;
43A90
;
44A05
;
45B05
;
45D05
;
45E10
;
47A68
;
47B35
;
60G35
;
60G60
;
62M15
;
62M20
;
73D30
;
81F15
;
86A15
;
93E10
;
93E11
;
Transmutation
;
transformation operators
;
Parseval formulas
;
eigenfunction expansions
;
Paley-Wiener theory
;
Riemann-Liouville and Weyl integrals
;
special functions
;
Gelfand-Levitan and Marčenko equations
;
generalized translation
;
generalized convolution
;
Volterra operators
;
Toeplitz operators
;
Wiener-Hopf equations
;
Bergman-Gilbert operators
;
Kontorovič-Lebedev inversion
;
generalized axially symmetric potential theory
;
canonical equations
;
deBranges spaces
;
random evolutions
;
scattering theory
;
inverse problems
;
filtering
;
smoothing
;
innovations
;
Darboux-Christoffel formulas
;
generating functions
;
reproducing kernels
;
random fields
;
linear stochastic estimation
;
spectral measures
;
orthogonal polynomials
;
least squares
;
etc
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This article represents a survey of transmutation ideas and their interaction with typical physical problems. For linear second-order differential operatorsP andQ one deals with canonical connectionsB:P→Q (transmutations) satisfyingQB=BP and the related transport of ‘structure’ between the theories ofP andQ. One can study in an intrinsic manner, e.g., Parseval formulas, eigenfunction expansions, integral transform, special functions, inverse problems, integral equations, and related stochastic filtering and estimation problems, etc. There are applications in virtually any area where such operators arise.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00046724
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