Eigenfunctions of the Fourier transform with specified zeros

Eigenvalues and Eigenfunctions of the Finite Fourier Transform

In recent times, considerable attention was focused on the computation of the eigenvalues and eigenfunctions of the Finite (truncated) Fourier Transform (FFT). An incentive to that a series of papers by Slepian and his collaborators at Bell labs was. The latest results published by Walter and Shen on sampling with the prolate spheroidal functions — the 1D FFT eigenfunctions — will necessary pro...

Zeros of eigenfunctions of some anharmonic oscillators

where P is a real even polynomial with positive leading coefficient, which is called a potential. The boundary condition is equivalent to y ∈ L(R) in this case. It is well-known that the spectrum is discrete, and all eigenvalues λ are real and simple, see, for example [3, 14]. The spectrum can be arranged in an increasing sequence λ0 < λ1 < . . .. Eigenfunctions y are real entire functions of o...

Zeros of real analytic ergodic Laplace eigenfunctions

Complex Zeros of Real Ergodic Eigenfunctions

We determine the limit distribution (as λ → ∞) of complex zeros for holomorphic continuations φCλ to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M, g) with ergodic geodesic flow. If {φjk} is an ergodic sequence of eigenfunctions, we prove the weak limit formula 1 λj φjk ] → i π∂∂|ξ|g, where φjk ] is the current of integration over the co...

GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.