Integral operators generated by exponential integrals

A Class of Integral Operators Generated by Random Variables

Let X be a random variable in Rp distributed symmetrically about zero with cumulants of order 4, 8, 12, . . . equal to zero. This class of random variables includes the multivariate normal. Consider the linear integral operator KX defined by KX g(x) = E [g(x+X)] = ∫ g(x + y) dP (X ≤ y) acting on the space of functions g : Cp → Cq with Taylor series expansions about zero. By Fredholm theory, non...

Bounds for Singular Fractional Integrals and Related Fourier Integral Operators

Ideals Generated by Exponential-Polynomials

In several problems in Harmonic Analysis, .and in Number Theory as well, lemmas on small values of holomorphic functions play an important role. Let us give first an example from Harmonic Analysis. distributions with compact support in 17% " whose Fourier transforms satisfy, in C " , a lower estimate of the form (0.2) with v, ,..., v, also distributions with compact support 131, 33). In many ex...

Motivic Exponential Integrals

Eigenvalue Decay of Integral Operators Generated by Power Series–like Kernels

We deduce decay rates for eigenvalues of integral operators generated by power serieslike kernels on a subset X of either Rq or Cq . A power series-like kernel is a Mercer kernel having a series expansion based on an orthogonal family { fα}α∈Zq+ in L 2(X ,μ) , in which μ is a complete measure on X . As so, we show that the eigenvalues of the integral operators are given by an explicit formula d...