A perturbed Whittaker–Kotelʼnikov–Shannon sampling theorem

A new minimax theorem and a perturbed James’s theorem

This paper is in two main parts. The first three sections give various result about bounded functions on an abstract set, while the last section is more functional–analytic in character. The main functional–analytic result is Theorem 14, which contains a sufficient condition for the minimax relation to hold for the canonical bilinear form on X × Y , where X is a nonempty convex subset of a real...

An Adiabatic Theorem for Singularly Perturbed Hamiltonians

The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian H0(t), satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form εH1(t). Here ε → 0 is the adiabaticity parameter and H1(t) is a self-adjoint operator defined on a smaller domain than the domain of H0(t). Thus the total hamiltonian H0(t) + εH1(t) d...

The Sampling Theorem and the Bandpass Theorem

A local limit theorem for perturbed random walks

The main result reported here is a Stone type local limit theorem for perturbed random walks 2, = S, + 5, when some slow variation conditions are imposed on 5,‘s.

A sampling theorem for shift-invariant subspace

A sampling theorem for regular sampling in shift invariant subspaces is established. The sufficient-necessary condition for which it holds is found. Then, the theorem is modified to the shift sampling in shiftinvariant subspaces by using the Zak transform. Finally, some examples are presented to show the generality of the theorem.