Open AccessCERTAIN ISOMETRIES RELATED TO THE BILATERAL LAPLACE TRANSFORM
Author(s) -
Semyon Yakubovich
Publication year - 2006
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2006.9637321
Subject(s) - laplace transform , mathematics , post's inversion formula , two sided laplace transform , mellin transform , pure mathematics , laplace transform applied to differential equations , inverse laplace transform , mathematical analysis , kernel (algebra) , type (biology) , transformation (genetics) , hilbert transform , fock space , inversion (geology) , space (punctuation) , reproducing kernel hilbert space , hilbert space , fourier transform , green's function for the three variable laplace equation , fractional fourier transform , computer science , fourier analysis , structural basin , ecology , chemistry , biology , operating system , paleontology , biochemistry , quantum mechanics , statistics , spectral density , physics , gene
We study certain isometries between Hilbert spaces, which are generated by the bilateral Laplace transformIn particular, we construct an analog of the Bargmann‐Fock type reproducing kernel Hilbert space related to this transformation. It is shown that under some integra‐bility conditions on $ the Laplace transform FF(z), z = x + iy is an entire function belonging to this space. The corresponding isometrical identities, representations of norms, analogs of the Paley‐Wiener and Plancherel's theorems are established. As an application this approach drives us to a different type of real inversion formulas for the bilateral Laplace transform in the mean convergence sense.