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Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed.
Bochner, S., 1933. Monotone Funktionen, Stieltjessche Integrale und harmonische Analyse. Mathematische Annalen 108, 378–410
1933
Earlier work this paper cites.
Schoenberg, I. J., Oct. 1938. Metric spaces and completely monotone functions. The Annals of Mathematics, Second Series 39 (4), 811–841
1938
Earlier work this paper cites.
Aronszajn, N., May 1950. Theory of reproducing kernels. Transactions of the American Mathematical Society 68 (3), 337–404
1950
Earlier work this paper cites.
Kramer, H. P., 1959. A generalized sampling theorem. Journal of Mathematics and Physics 38, 68–72
1959
Earlier work this paper cites.
Schwartz, L., 1964. Sous-espaces hilbertiens d’espaces vectoriels topologiques et noyaux associés (noyaux reproduisants). Journal d’Analyse Mathématique 13, 115–256
1964
Earlier work this paper cites.
Jerri, A. J., 1977. The Shannon sampling theorem—its various extensions and applications: A tutorial review. Proceedings of the IEEE 65, 1565–1596
1977
Earlier work this paper cites.
Nielsen, O. A., 1980. Direct Integral Theory. Lecture notes in pure and applied mathematics. Marcel Dekker, Inc., New York
1980
Cited alongside, same era.
Saitoh, S., 1983. Hilbert spaces induced by Hilbert space valued functions. Proceedings of the American Mathematical Society 58(A), 361–364
1983
Cited alongside, same era.
Saitoh, S., 1987. Integral transforms, reproducing kernels and their applications. Vol. 369 of Pitman Research Notes in Mathematics Series. Addison Wesley Longman Limited, Harlow
1987
Cited alongside, same era.
Yaglom, A. M., 1987. Correlation Theory of Stationary and Related Random Functions. Vol. 1 of Springer series in statistics. Springer, New York
1987
Cited alongside, same era.
Nashed, M. Z., Walter, G. G., 1991. General sampling theorems for functions in reproducing kernel Hilbert spaces. Mathematics of Control, Signals, and Systems 4, 363–390
Buhmann, M. D., 1998. Radial functions on compact support. Proceedings of the Edinburgh Mathematical Society 41, 33–46
1998
Later among the works it cites.
Gneiting, T., 1999. Radial positive definite functions generated by Euclid’s hat. Journal of Multivariate Analysis 69, 88–119
1999
Later among the works it cites.
Schölkopf, B., Herbrich, R., Smola, A. J., Williamson, R., 2000. A generalized representer theorem. Tech. Rep. NC2-TR-2000-81, NeuroCOLT2
2000
Later among the works it cites.
Jetter, K., Plonka, G., 2001. A survey on L2-approximation order from shift-invariant spaces. In: Dyn, N., Leviatan, D., Levin, D., Pinkus, A. (Eds.), Multivariate Approximation and Applications. Cambridge University Press, pp. 73–111
2001
Later among the works it cites.
Wendland, H., 2005. Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge
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1991
Cited alongside, same era.
Engl, H. W., Hanke, M., Neubauer, A., 1996. Regularization of Inverse Problems. Vol. 375 of Mathematics and Its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands
1996
Cited alongside, same era.
2005
Later among the works it cites.
Carmeli, C., de Vito, E., Tiogo, A., 2006. Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem. Analysis and Applications 4 (4), 377–408
2006
Later among the works it cites.