A note on analytic continuation of characteristic functions

A note on harmonic continuation of characteristic function

We propose a necessary and sufficient condition for a real-valued function on the real line to be a characteristic function of a probability measures. The statement is given in terms of harmonic functions and completely monotonic functions.

Analytic continuation of a biholomorphic mapping

We present a new proof of Pinchuk's theorem on the analytic continuation of a biholomorphic mapping from a strongly pseudoconvex analytic real hypersurface to a compact strongly pseudoconvex analytic real hypersurface in a complex euclidean space.

局部zeta函数到带切口复平面的解析延拓：一维情形

Analytic continuation of local zeta functions to a slit complex plane: the one-dimensional case

本文针对一维局部zeta函数，给出其在沿负实轴切割的复平面上存在全纯延拓的充分条件。

Hypergeometric reproducing kernels and analytic continuation from a half-line

Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized hypergeometric function are completely characterized. A particular space generated by the modified Bessel function kernel is utilized to derive an analytic continuation formula for functions on $R^+$ using the best approximation theorem of S. Saitoh. As a by-product several new area integrals involving Bessel functions are explicitly evaluated

Analytic Continuation of Hypergeometric Functions in the Resonant Case

We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant case, there are necessarily logarithmic solutions. We apply the result to Picard-Fuchs equations of certain one--parameter families of Calabi--Yau manifolds, known as the mirror quartic and the mirror quintic.

Regularized Limit, analytic continuation and finite-part integration

Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately induced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the relationship is established between the analytic continuation of the Mellin transform and the finite-part of the resulting divergent integral when the Mellin integral is extended beyond its strip of analyticity. It is settled …