Fractional weyl-riesz integrodifferentiation of periodic functions of two variables via the periodization of the riesz kernel

Applicable Analysis

Volumn 82, Issue 3, 2003, Pages 269-299

  Samko, Stefan G ^a  

^a UNIVERSIDADE DO ALGARVE   (Portugal)

Author keywords

Fractional Integration; Periodic Convolutions; Periodization; Weyl Integration

Indexed keywords

EID: 35348945207     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/0003681031000094889     Document Type: Article

References (21)

1. Anaya, M., 1974/75. Periodizacion de integrales singulares. Math. Notas, 24: 39–55.
2. Benedetto, J.J., 1997. Harmonie Analysis and Applications, Boca Raton: CRC Press.
3. Butzer, P.L., and Gessinger, A., 1997. The approximate sampling theorem, Poisson's sum formula, a decomposition theorem for Parseval's equation and their interconnections. The heritage of P.L. Chebyshev: a Festschrift in honor of the 70th birthday of T.J. Rivlin. Ann. Numer. Math., 4(1-4): 143–160.
4. Butzer, Paul L., and Nessel, R.J., 1971. Fourier analysis and approximation. One-dimensional theory. Pure and Applied Mathematics, Vol. 40, New York-London: Academic Press.
5. Paul, L. Butzer, and Stens, R.L., The Poisson summation formula, Whittaker's cardinal series and approximate integration. Second Edmonton conference on approximation theory. 1982, Edmonton, Alta. pp. 19–36. Providence, RI CMS Conf. Proc., 3, Amer. Math. Soc.
6. Gorenflo, R., and Mainardi, F., 1998. Random walk models for spacefractional diffusion processes. Fract. CaIc. Appl. Anal., 1(2): 167–191.
7. Gradshtein, I.S., and Ryzhik, I.M., 1994. Tables of Integrals, Sums, Series and Products, 5th Edn., Boston: Academic Press, Inc.
8. Hilfer, R., ed. 2000. Applications of Fractional Calculus in Physics, River Edge, NJ: World Scientific Publishing Co., Inc.
9. Hotzel, R., and Fliess, M., 1998. On linear systems with a fractional derivation: introductory theory and examples. Delay systems (Lille, 1996). Math. Comput. Simulation, 45(3-4): 385–395.
10. Jacob, N., and Krageloh, A., 2002. Feller semigroups on C00 (Rr* T) generated by Weyl fractional derivatives and pseudo-differential operators. Fract. CaIc. Appl. Anal., 5(1): 77–116.
11. Kubas, A.A., and Trujillo, J.J., 2001. Differential equations of fractional order: methods, results and problems, I. Appl. Anal, 78(1-2): 153–192.
12. Liouville, J., 1832. Mémoire sur quelques questions e géométrie e de mécanique, et sur un noveaux genre de calcul pour résoudre ces questions. J. l'Ecole Roy. Polytechn., 13(21): 1–69.
13. Liouville, J., 1832. Mémoire sur le calcul des différentielles à indice quelconques. J. l'Ecole Roy. Polytechn., 13(21): 71–162.
14. Liouville, J., 1834. Mémoire sur une formule d'analyse. J. far Reine und Angew. Math., 12(4): 273–287.
15. Machado, J.A.T., 2001. Discrete-time fractional-order controllers. Fract. CaIc. Appl. Anal., 4(1): 47–66.
16. Mikolas, M., 1959. Differentiation and integration of complex order of functions represented by trigonometrical series and generalized zeta-function. Acta Math. Acad. Sci. Hung., 10(1-2): 77–124.
17. Samko, S.O., 2002. Hypersingular Integrals and Their Applications. "Taylor and Francis", Series Analytic Methods and Special Functions Vol. 5, London-New York
18. Samko, S.O., Kubas, A.A., and Marichev, O.I., 1993. Fractional Integrals and Derivatives. Theory and Applications, London-New York: Gordon and Breach. Sei. Publ.
19. Weyl, H., 1917. Bemerkungen zum Begriff des Differentialquotienten gebrochener Ordnung. Vierteljahresschrift der Naturforschenden Gesellschaft in Zurich., 62(1): 296–302.
20. Whittaker, ET., and Watson, G.N., 1927. A Course in Modem Analysis, Vol. 2. Transcendental Functions, Vol. 2, Cambridge: Cambridge University Press.
21. Zygmund, A., 1968. Trigonometric Series, Vol. 2, London - New York: Cambridge University Press.