bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Belhadj, M. and Betancor, J. J.:
Entire elliptic Hankel convolution equations
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.3, p. 717-737, Unione Matematica Italiana (English)
pdf (304 Kb), djvu (253 Kb). | MR2014829 | Zbl 1179.46036

Sunto

In questo lavoro caratterizziamo gli operatori di convoluzione di Hankel ellittici interi su distribuzioni temperate in termini della crescita delle loro trasformate di Hankel.
Referenze Bibliografiche
[1] G. ALTENBURG, Bessel-Transformationen in Räumen von Grundfunktionen über dem Intervall $\Omega = (0,+\infty)$ und deren Dualraumen, Math. Nachr., 108 (1982), 197-218. | MR 695127 | Zbl 0528.46035
[2] M. BELHADJ-J. J. BETANCOR, Hankel convolution operators on entire functions and distributions, J. Math. Anal. Appl., 276 (2002), 40-63. | MR 1944335 | Zbl 1012.44003
[3] J. J. BETANCOR-I. MARRERO, Multipliers of Hankel transformable generalized functions, Comment. Math. Univ. Carolinae, 33 (3) (1992), 389-401. | fulltext mini-dml | MR 1209282 | Zbl 0801.46047
[4] J. J. BETANCOR-I. MARRERO, The Hankel convolution and the Zemanian spaces $\beta_\mu$ and $\beta'_\mu$, Math. Nachr., 160 (1993), 277-298. | MR 1245003 | Zbl 0796.46023
[5] J. J. BETANCOR-I. MARRERO, Structure and convergence in certain spaces of distributions and the generalized Hankel convolution, Math. Japonica, 38 (6) (1993), 1141-1155. | MR 1250341 | Zbl 0795.46023
[6] J. J. BETANCOR-I. MARRERO, Some properties of Hankel convolution operators, Canad. Math. Bull., 36 (4) (1993), 398-406. | MR 1245312 | Zbl 0795.46024
[7] J. J. BETANCOR-I. MARRERO, On the topology of the space of Hankel convolution operators, J. Math. Anal. Appl., 201 (1996), 994-1001. | MR 1400576 | Zbl 0905.46024
[8] J. J. BETANCOR-L. RODRÍGUEZ-MESA, Hankel convolution on distribution spaces with exponential growth, Studia Math., 121 (1) (1996), 35-52. | fulltext mini-dml | MR 1414893 | Zbl 0862.46021
[9] J. J. BETANCOR-L. RODRÍGUEZ-MESA, On Hankel convolution equations in distribution spaces, Rocky Mountain J. Math., 29 (1) (1999), 93-114. | fulltext mini-dml | MR 1687657 | Zbl 0926.46034
[10] F. M. CHOLEWINSKI, A Hankel Convolution Complex Inversion Theory, Mem. Amer. Math. Soc., 58 (1965). | MR 180813 | Zbl 0137.30901
[11] F. M. CHOLEWINSKI, Generalized Fock spaces and associated operators, SIAM J. Math. Anal., 15 (1) (1984), 177-202. | MR 728694 | Zbl 0596.46017
[12] S. J. L. VON EIJNDHOVEN-J. DE GRAAF, Some results on Hankel invariant distribution spaces, Proc. Kon. Ned. Akad. van Wetensch. A, 86 (1) (1983), 77-87. | MR 695592 | Zbl 0516.46023
[13] S. J. L. VON EIJNDHOVEN-M. J. KERKHOF, The Hankel transformation and spaces of $W$-type, Reports on Appl. and Numer. Analysis, 10, Dept. of Maths. and Comp. Sci., Eindhoven Univ. of Tech. (1988).
[14] L. EHRENPREIS, Solution of some problem of division, Part IV. Invertible and elliptic operators, Amer. J. Maths., 82 (1960), 522-588. | MR 119082 | Zbl 0098.08401
[15] A. ERDÉLYI, Tables of integral transforms, II, McGraw Hill, New York, 1953.
[16] G. GODEFROY-J.H. SHAPIRO, Operators with dense, invariant, cyclic vector manifolds, J. Functional Anal., 98 (1991), 229-269. | MR 1111569 | Zbl 0732.47016
[17] D. T. HAIMO, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc., 116 (1965), 330-375. | MR 185379 | Zbl 0135.33502
[18] C. S. HERZ, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. USA, 40 (1954), 996-999. | MR 63477 | Zbl 0059.09901
[19] I. I. JR. HIRSCHMAN, Variation diminishing Hankel transforms, J. Analyse Math., 8 (1960/61), 307-336. | MR 157197 | Zbl 0099.31301
[20] J. HORVATH, Topological Vector Spaces and Distributions, I, Addison-Wesley, Reading, Massachusetts (1966). | MR 205028 | Zbl 0143.15101
[21] I. MARRERO-J. J. BETANCOR, Hankel convolution of generalized functions, Rendiconti di Matematica, 15 (1995), 351-380. | MR 1362778 | Zbl 0833.46026
[22] L. SCHWARTZ, Theorie des distributions, Hermann, Paris, 1978. | MR 209834 | Zbl 0399.46028
[23] J. DE SOUSA-PINTO, A generalized Hankel convolution, SIAM J. Appl. Math., 16 (1985), 1335-1346. | MR 807914 | Zbl 0592.46038
[24] K. TRIMÉCHE, Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur $(0, \infty)$, J. Math. Pures Appl., 60 (9) (1981), 51-98. | MR 616008 | Zbl 0416.44002
[25] G. N. WATSON, A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge, 1959. | MR 1349110 | Zbl 0174.36202 | Jbk 48.0412.02
[26] A. H. ZEMANIAN, A distributional Hankel transformation, SIAM J. Appl. Math., 14 (1966), 561-576. | MR 201930 | Zbl 0154.13803
[27] A. H. ZEMANIAN, The Hankel transformations of certain distributions of rapid growth, J. SIAM Appl. Math., 14 (4) (1966), 678-690. | MR 211211 | Zbl 0154.13804
[28] A. H. ZEMANIAN, Generalized integral transformations, Interscience Publishers, New York, 1968. | MR 423007 | Zbl 0181.12701
[29] Z. ZIELEZNY, Hypoelliptic and entire elliptic convolution equations in subspaces of the spaces of distributions (I), Studia Math., 28 (1967), 317-332. | fulltext mini-dml | MR 222476 | Zbl 0181.42201

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali