Related papers: A remark on the Sibony function

We consider the Dirichlet-Neumann operator for a nearly spherical domain in R^n, and prove sharp analytic and tame estimates in Sobolev class. The novelty of this paper concerns technical improvements, the most important of which are the…

We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a…

With no criteria of the index type, it is proved the existence of a solution for the Riemann-Hilbert problem in the fairly general setting of arbitrary Jordan domains, measurable coefficients and measurable boundary data. The theorem is…

We construct a Cauchy type formula on open subdomains of Riemann surfaces

We propose a formula for finding the horizontal, oblique or curvilinear asymptote of any rational polynomial function of any positive degree, as a sum of matrix determinants formed directly from the coefficients of the terms in the given…

This note contains a short proof of the functional equation for the zeta function.

We establish the Fa\`a di Bruno formula, in the sense of almost everywhere equality, for derivatives of the composed function $f \circ g$, for all function $f : R \rightarrow R$ such that $f$ acts on $W^m_p(R^n)$ by composition, and all $g…

This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

Using the functional associated with the optimal Wente inequality for pairs of functions on 2-dimensional domains, we show the existence of solutions to the H-system on an annulus satisfying Neumann boundary conditions.

Functional determinants on various domains of the sphere and flat space are presented for scalar and spinor fields.

We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds, and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.

In this note, we establish a Vorono\"i--Oppenheim summation formula for divisor functions over an arbitrary number field.

In this paper we evaluate sums and integrals of products of Fubini polynomials and have new explicit formulas for Fubini polynomials and numbers. As a consequence of these results new explicit formulas for p-Bernoulli numbers and…

The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation…

A simple application of the semipositivity.

We generalize Warnaar's elliptic extension of a Macdonald multiparameter summation formula to Riemann surfaces of arbitrary genus.

We prove several formulas for the distribution of positive roots.

In this paper, we give an explicit formula of the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three applications of the explicit formula are given. First, we…