Journal
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
Volume 117, Issue 1, Pages -Publisher
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s13398-022-01335-0
Keywords
Mehler-Fock transform; Operational calculus; Distributions of compact support; Associated Legendre function; Differential operator; Regular distributions
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In this paper, we analyze an operational calculus based on the Mehler-Fock type index transform on distributions of compact support over the interval (1,8). Using this transform, we obtain a distribution f on the interval (1,8) that satisfies an equation of the form P (A(t)')u = g, where P is any polynomial with no zeros in the interval (-infinity,- 1/4], A(t)(') is the adjoint of the differential operator At = Dt (t2 - 1) Dt, the distribution g has compact support on (1,infinity), and u is an unknown distribution on (1,infinity).
In this paper, we present a systematic analysis of an operational calculus which is based upon a Mehler-Fock type index transform on distributions of compact support over the interval (1,8). By means of this transform, we obtain a distribution f on the interval (1,8), which satisfies an equation of the type P (A(t)')u = g, where P denotes any polynomial with no zeros in the interval (-infinity,- 1/4], A(t)(') represents the adjoint of the differential operator At = Dt (t2 - 1) Dt, the distribution g has compact support on (1,infinity) and u is an unknown distribution on (1,infinity).
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