Criteria of pólya type for radial positive definite functions

Proceedings of the American Mathematical Society

Volumn 129, Issue 8, 2001, Pages 2309-2318

  Gneiting, Tilmann ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041043233     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-01-05839-7     Document Type: Article

References (36)

1. Askey, R., Radial Characteristic Functions, University of Wisconsin-Madison, Mathematics Research Center, 1262, 1973.
2. Askey, R., Some characteristic functions of unimodal distributions, J. Math. Anal. Appl., 50 (1975), 465-469. MR 51:6910
3. Berens, H. and Xu, Y., l-1 summability of multiple Fourier integrals and positivity, Math. Proc. Cambridge Philos. Soc., 122 (1997), 149-172. MR 98g:42035
4. Bochner, S. and Chandrasekharan, K., Fourier Transforms, Princeton University Press, 1949. MR 11:173d
5. Gneiting, T., On α-symmetric multivariate characteristic functions, J. Multivariate Anal., 64 (1998), 131-147. MR 99h:60025
6. Gneiting, T., On the derivatives of radial positive definite functions, J. Math. Anal. Appl., 236 (1999), 86-93. MR 2000k:42012
7. Gneiting, T., Radial positive definite functions generated by Euclid's hat, J. Multivariate Anal., 69 (1999), 88-119. MR 2000g:60022
8. 2, Exposition. Math., 17 (1999), 181-183. MR 2000e:60024
9. Gneiting, T., Kuttner's problem and a Pólya type criterion for characteristic functions, Proc. Amer. Math. Soc., 128 (2000), 1721-1728. MR 2000j:42016
10. Golubov, B. I., On Abel-Poisson type and Riesz means, Anal. Math., 7 (1981), 161-184. MR 83b:42015
11. Heal, K. M. and Hansen, M. L. and Rickard, K. M., Maple V Learning Guide, Springer, New York, 1996.
12. Koldobskiǐ, A. L., Schoenberg's problem on positive definite functions, St. Petersburg Math. J., 3 (1992), 563-570. MR 93c:42014
13. Koldobsky, A., Positive definite functions, stable measures, and isometrics on Banach spaces, Interaction Between Functional Analysis, Harmonic Analysis, and Probability, Lecture Notes in Pure and Appl. Math., 175, Marcel Dekker, 1996, 275-290. MR 96k:46016
14. Kuttner, B., On the Riesz means of a Fourier series (II), J. London Math. Soc., 19 (1944), 77-84. MR 7:59d
15. n+1, Ann. Inst. H. Poincaré Probab. Statist., 22 (1986), 169-174. MR 87i:42027
16. Lévy, P. , Extensions d'un théorème de D. Dugué et M. Girault, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 1 (1962), 159-173. MR 26:3096
17. Liflyand, E. R., Ramm, A. G. and Zaslavsky, A. I., Estimates from below for Lebesgue constants, J. Fourier Anal. Appl., 2 (1996), 287-301. MR 97g:42007
18. Matheron, G., Les variables régionalisées et leur estimation, Masson, Paris, 1965.
19. α-spaces, Dissertationcs Math., 358 (1996), 1-91. MR 97k:60040b
20. Misiewicz, J. K. and Richards, D. St. P., Positivity of integrals of Bessel functions, SIAM J. Math. Anal., 25 (1994), 596-601. MR 95i:33004
21. Misiewicz, J. K. and Scheffer, C. L., Pseudo isotropic measures, Nieuw Arch. Wisk. IV, 8 (1990), 111-152. MR 92e:60007
22. Mittal, Y., A class of isotropic covariance functions, Pacific J. Math., 64 (1976), 517-538. MR 54:14068
23. Pasenchenko, O. Yu., Sufficient conditions for the characteristic function of a two-dimensional isotropic distribution, Theory Probab. Math. Statist., 53 (1996), 149-152. MR 98b:60033
24. Pólya, G., Remarks on Characteristic Functions, Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 1949, 115-123. MR 10:463c
25. Richards, D. St. P., Positive definite symmetric functions on finite dimensional spaces. 1. Applications of the Radon transform, J. Multivariate Anal., 19 (1986), 280-298. MR 88c:60043a
26. Sasvári, Z., On a classical theorem in the theory of Fourier integrals, Proc. Amer. Math. Soc., 126 (1998), 711-713. MR 98i:60013
27. Schoenberg, I. J., Metric spaces and completely monotone functions, Ann. of Math., 39 (1938), 811-841.
28. Schoenberg, I. J., Metric spaces and positive definite functions, Trans. Amer. Math. Soc., 44 (1938), 522-536. CMP 95:18
29. Trigub, R. M., A criterion for a characteristic function and a Polyá type criterion for radial functions of several variables, Theory Probab. Appl., 34 (1989), 738-742. MR 91f:60033
30. Wendland, H., Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Adv. Comput. Math., 4 (1995), 389-396. MR 96h:41025
31. Williamson, R. E., Multiply monotone functions and their Laplace transforms, Duke Math. J., 23 (1956), 189-207. MR 17:1061d
32. Wintner, A., On a family of Fourier transforms, Bull. Amer. Math. Soc., 48 (1942), 304-308. MR 3:232a
33. Wu, Z., Compactly supported positive definite radial functions, Adv. Comput. Math., 4 (1995), 283-292. MR 97g:65031
34. Zastavnyi, V. P., Positive-definite functions that depend on a norm, Russian Acad. Sci. Dokl. Math., 46 (1993), 112-114. MR 94k:42026
35. Zastavnyi, V. P., On positive definiteness of some functions, Dokl. Math., 365 (1999), 159-161. MR 2000i:42005
36. Zastavnyi, V. P., On positive definiteness of some functions, J. Multivariate Anal., 73 (2000), 55-81. CMP 2000:14