Relative reproducing kernel Hilbert spaces

Authors:
Daniel Alpay, Palle Jorgensen and Dan Volok

Journal:
Proc. Amer. Math. Soc. **142** (2014), 3889-3895

MSC (2010):
Primary 46E22, 47B32, 42A82

Published electronically:
July 17, 2014

MathSciNet review:
3251728

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Abstract | References | Similar Articles | Additional Information

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.

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Palle
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Additional Information

**Daniel Alpay**

Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel

Email:
dany@math.bgu.ac.il

**Palle Jorgensen**

Affiliation:
Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, Iowa 52242-1419

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

DOI:
https://doi.org/10.1090/S0002-9939-2014-12121-6

Keywords:
Reproducing kernels,
conditionally negative functions,
unbounded operators

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

Article copyright:
© Copyright 2014
American Mathematical Society