In this paper, various growth rates and oscillation conditions for entire functions of exponential type π are given which ensure validity of the classical cardinal series. Among other applications, a… (More)

Suppose u is a function on a domain inRn all of whosemth order distributional derivatives are inLp( ) and m is sufficiently large to imply that u is continuous. If the values of u on a sufficiently… (More)

We consider the problem of reconstruction of functions f from generalized Paley–Wiener spaces in terms of their values on complete interpolating sequence {zn}. We characterize the set of data… (More)

We investigate functions φ(x) whose translates {φ(x−k)}, where k runs through the integer lattice Z, provide a system of orthonormal sampling functions. The cardinal sine, whose important role in the… (More)

We outline a method of image magnification based on parametric families of fast orthogonal transforms which arise from the multiresolutionlwavelet paradigm of Mallat and Meyer. The essential idea is… (More)

We present extensions of the classical Poisson summation formula in which the sequence of sampling knots, normally a lattice, can be taken from a relatively wide class of sequences.

We establish properties of and propose a conjecture concerning P m(S(x + m)) 2 where S is a piecewise polynomial cardinal spline in L(R). 2000 Mathematics subject classification: 65A15, 62G07

Growth conditions are given on the samples f(n), n = 0, ±1, ±2, ..., of an entire function f(z) of exponential type less than π that imply that the corresponding cardinal sine series converges. These… (More)