A note on the Gaussian cardinal-interpolation operator Academic Article

abstract

• Suppose is a positive number, and let , xRd, denote the d-dimensional Gaussian. Basic theory of cardinal interpolation asserts the existence of a unique function , xRd, satisfying the interpolatory conditions , kZd, and decaying exponentially for large argument. In particular, the Gaussian cardinal-interpolation operator, given by , xRd, , is a well-defned linear map from 2(Zd) into L2(Rd). It is shown here that its associated operator-norm is , implying, in particular, that is contractive. Some sidelights are also presented.

authors

• Sivakumar, Natarajan

published proceedings

• PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

author list (cited authors)

• Sivakumar, N.

citation count

• 9

complete list of authors

• Sivakumar, N

publication date

• February 1997

publisher

• Cambridge University Press (CUP)  Publisher

published in

• Proceedings of the Edinburgh Mathematical Society  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1017/S0013091500023506

start page

• 137

end page

• 149

volume

• 40

issue

• 1

URL

• http://dx.doi.org/10.1017/s0013091500023506