Extensions of the Poisson Summation Formula

Journal of Mathematical Analysis and Applications

Volumn 218, Issue 2, 1998, Pages 581-606

  Duran A L ^a   Estrada, R ^a   Kanwal, R P ^b  

^a UNIVERSIDAD DE COSTA RICA   (Costa Rica)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010344450     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5767     Document Type: Article

References (23)

1. Apostel T. M. Introduction to Analytic Number Theory. 1976;Springer-Verlag.
2. Berndt B. C., Evans R. J. Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook. J. Reine Angew Math. 361:1985;118-134.
3. Boersma J. A nonharmonic trigonometric series. SIAM Rev. 37:1995;443-445.
4. Estrada R. The asymptotic expansion of certain series considered by Ramanujan. Appl. Anal. 43:1992;191-228.
5. R. Estrada, The Cesàro behavior of distributions.
6. R. Estrada, S. A. Fulling, Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
7. Estrada R., Kanwal R. P. Regularization, pseudofunction and Hadamad finite part. J. Math. Anal. Appl. 141:1989;195-207.
8. Estrada R., Kanwal R. P. A distributional theory for asymptotic expansions. Proc. Roy. Soc. London Ser. A. 428:1990;399-430.
9. Estrada R., Kanwal R. P. Asymptotic Analysis: A Distributional Approach. 1994;Birkhäuser, Boston.
10. Gelfand I. M., Shilov G. E. Generalized Functions. 1964;Academic Press.
11. Glasser M. L. A nonharmonic trigonometric series. SIAM Rev. 37:1995;443.
12. Grossman A., Lupias G., Stein E. M. An algebra of pseudodifferential operators and quantum mechanics in phase space. Ann. Inst. Fourier (Grenoble). 18:1968;343-368.
13. Hardy G. H., Littlewood J. E. Some problems of diophantine approximation. Acta Math. 37:1914;155-238.
14. Henkel M., Weston R. A. On alternating multiple sums. SIAM Rev. 34:1992;496.
15. Kanwal R. P. Generalized Functions: Theory and Technique. 1983;Academic Press.
16. Lojasiewicz S. Sur la valeur et la limite d'une distribution en un point. Studia Math. 16:1957;1-36.
17. Ortner N., Wagner P. Fundamental solutions of hyperbolic differential operators and the Poisson integral formula. Integral Transf. Spec. Funct. 1:1993;183-196.
18. Ortner N., Wagner P. Series, the convergence of which should be interpreted in the sense of L. Schwartz's distributions. SIAM Rev. 37:1995;428-435.
19. Pilipovic S. Quasiasymptotic expansion and the Laplace transform. Appl. Anal. 35:1990;247-261.
20. Ramanujan S. Notebooks. 1956;Tata Institute, Bombay.
21. Schwartz L. Théorie des Distributions. 1966;Hermann, Paris.
22. Titchmarsh E. C. The Theory of the Riemann Zeta-Function. 1951;Clarendon, Oxford.
23. Vladimirov V. S., Drozhinov Y. N., Zavgalov B. I. Multidimensional Tauberian Theorems for Generalized Functions. 1986;Nauka, Moscow.