Local approximation for the phase velocity transform

Physics of Plasmas

Volumn 6, Issue 4, 1999, Pages 1059-1064

  Mattor, Nathan ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0343276014     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.873353     Document Type: Article

References (9)

1. N. Mattor, Phys. Plasmas 5, 1822 (1998).
2. N. Mattor, Phys. Plasmas 6, 1065 (1999).
3. p,t) is used instead for clarity in later generalizations.
4. p this restriction is lifted. Since the basic transform is based on a Fourier space-time transform with no additional assumption (other than convergence), then the PVT applies to the same class of functions. The closely related k-plane transform does have some existence and uniqueness questions, but these appear to be mainly mathematical. [See Ahmed I. Zayed, Handbook of Function and Generalized Function Transformations (CRC Press, Boca Raton, 1996), p. 562.]
5. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978) contains several good discussions about local approximations.
6. Formally the domain in k becomes discrete, but this is an unimportant detail for this discussion since the limit kΔ→∞ is eventually taken.
7. Ahmed I. Zayed, Handbook of Function and Generalized Function Transformations (CRC Press, Boca Raton, 1996), pp. 273-287. 531-555, and 557-579.
8. x′ in Eq. (14); this information is lost and noninvertible.
9. Gregory Beylkin, Commun. Pure Appl. Math. 37, 579 (1984).