An oscillatory singular integral operator with polynomial phase

Self-adjointness of Cauchy Singular Integral Operator

We extend Krupnik’s criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion. Let G+ be a finitely connected domain bounded by the rectifiable curve C = ∂G+, G− = C \ clos G+ and ∞ ∈ G−. Suppose also that w(z), z ∈ C is a nonnegative weight such that w(z) 6≡...

Oscillatory Integral Operators with Homogeneous Polynomial Phases in Several Variables

We obtain L decay estimates in λ for oscillatory integral operators Tλ whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of (2+2)–dimensions for any m, while in higher dimensions the result is sharp for m sufficiently large. The proof for large m follows from essentially algebraic considerat...

Simply Nondegenerate Multilinear Oscillatory Integral Operators with Smooth Phase

Here > 0 is to be independent of η(x). In [CLTaTh] this question was considered in considerable depth, and attention was focused on the case where S(x) is a polynomial. Here we will extend several of their results to the general smooth case. When the πj are all projections onto 1 dimensional spaces and one considers L norms instead of L∞ norms, much additional work has been done, such as [PS] [...

On an integral operator

In this paper we define a general integral operator for analytic functions in the open unit disk and we determine some conditions for univalence of this integral operator.

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions