Relative reproducing kernel Hilbert spaces
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- by Daniel Alpay, Palle Jorgensen and Dan Volok PDF
- Proc. Amer. Math. Soc. 142 (2014), 3889-3895 Request permission
Abstract:
We introduce a reproducing kernel structure for Hilbert spaces of functions where differences of point evaluations are bounded. The associated reproducing kernels are characterized in terms of conditionally negative functions.References
- D. Alpay and T. M. Mills, A family of Hilbert spaces which are not reproducing kernel Hilbert spaces, J. Anal. Appl. 1 (2003), no. 2, 107–111. MR 1986785
- N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR 51437, DOI 10.1090/S0002-9947-1950-0051437-7
- William Arveson, An addition formula for the index of semigroups of endomorphisms of $B(H)$, Pacific J. Math. 137 (1989), no. 1, 19–36. MR 983326
- Kendall Atkinson and Weimin Han, Spherical harmonics and approximations on the unit sphere: an introduction, Lecture Notes in Mathematics, vol. 2044, Springer, Heidelberg, 2012. MR 2934227, DOI 10.1007/978-3-642-25983-8
- Christian Berg, Jens Peter Reus Christensen, and Paul Ressel, Harmonic analysis on semigroups, Graduate Texts in Mathematics, vol. 100, Springer-Verlag, New York, 1984. Theory of positive definite and related functions. MR 747302, DOI 10.1007/978-1-4612-1128-0
- W. Donoghue and P. Masani, A class of invalid assertions concerning function Hilbert spaces, Bol. Soc. Mat. Mexicana (2) 28 (1983), no. 2, 77–80. MR 791090
- Peter Giesl and Holger Wendland, Approximating the basin of attraction of time-periodic ODEs by meshless collocation of a Cauchy problem, Discrete Contin. Dyn. Syst. Dynamical systems, differential equations and applications. 7th AIMS Conference, suppl. (2009), 259–268. MR 2641402
- Palle E. T. Jorgensen and Erin P. J. Pearse, A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks, Israel J. Math. 196 (2013), no. 1, 113–160. MR 3096586, DOI 10.1007/s11856-012-0165-2
- Palle E. T. Jorgensen and Erin Peter James Pearse, A Hilbert space approach to effective resistance metric, Complex Anal. Oper. Theory 4 (2010), no. 4, 975–1013. MR 2735315, DOI 10.1007/s11785-009-0041-1
- Palle E. T. Jorgensen and Erin Peter James Pearse. Operator theory of electrical resistance networks, arXiv:0806.3881, November 2009.
- Holger Wendland, Scattered data approximation, Cambridge Monographs on Applied and Computational Mathematics, vol. 17, Cambridge University Press, Cambridge, 2005. MR 2131724
- J. D. Maitland Wright, All operators on a Hilbert space are bounded, Bull. Amer. Math. Soc. 79 (1973), 1247–1250. MR 328649, DOI 10.1090/S0002-9904-1973-13399-3
Additional Information
- Daniel Alpay
- Affiliation: Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel
- MR Author ID: 223612
- Email: dany@math.bgu.ac.il
- Palle Jorgensen
- Affiliation: Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, Iowa 52242-1419
- MR Author ID: 95800
- ORCID: 0000-0003-2681-5753
- Email: jorgen@math.uiowa.edu
- Dan Volok
- Affiliation: Department of Mathematics, 138 Cardwell Hall, Kansas State University, Manhattan, Kansas 66506
- Email: danvolok@math.ksu.edu
- Received by editor(s): November 7, 2012
- Received by editor(s) in revised form: December 6, 2012
- Published electronically: July 17, 2014
- Additional Notes: The first author thanks the Earl Katz family for endowing the chair which supported his research. The research of the authors was supported in part by the Binational Science Foundation grant No. 2010117.
- Communicated by: Pamela B. Gorkin
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 3889-3895
- MSC (2010): Primary 46E22, 47B32, 42A82
- DOI: https://doi.org/10.1090/S0002-9939-2014-12121-6
- MathSciNet review: 3251728