Related papers: Holomorphic Extension of Eigenfunctions

In this paper, we address the problem of determining a function in terms of its orbital integrals on Lorentzian symmetric spaces. It has been solved by S. Helgason for even-dimensional isotropic Lorentzian symmetric spaces via a limit…

Real analytic functions on the boundary of the sphere which have separate holomorphic extension along the complex lines through a boundary point have holomorphic extension to the ball. This was proved in a previous preprint by an argument…

In this paper, we continue to develop the theory of free holomorphic functions on noncommutative regular polydomains. We find analogues of several classical results from complex analysis such as Abel theorem, Hadamard formula, Cauchy…

We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ depend real…

We investigate H\"ormander spectral multiplier theorems as they hold on $X = L^p(\Omega),\: 1 < p < \infty,$ for many self-adjoint elliptic differential operators $A$ including the standard Laplacian on $\R^d.$ A strengthened matricial…

Here we prove an isoperimetric inequality for the harmonic mean of the first $N-1$ non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of $\mathbb{S}^N$.

Let $h$ be a harmonic function defined on a spherical disk. It is shown that $\Delta^k |h|^2$ is nonnegative for all $k\in \mathbb{N}$ where $\Delta$ is the Laplace-Beltrami operator. This fact is generalized to harmonic functions defined…

Let $B_{R}$ be the ball in the euclidean space $\mathbb{R}^{n}$ with center 0 and radius $R$ and let $f$ be a complex-valued, infinitely differentiable function on $B_{R}.$ We show that the Laplace-Fourier series of $f$ has a holomorphic…

Let $G $ be a noncompact semisimple Lie group with finite centre. Let $X=G/K$ be the associated Riemannian symmetric space and assume that $X$ is of rank one. The spectral projections associated to the Laplace-Beltrami operator are given by…

In this note we will present an extension of the Krein-Rutman theorem for an abstract nonlinear, compact, positively 1-homogeneous, monotone non-decreasing operators on a Banach space and apply the result to many nonlinear elliptic partial…

Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…

We present a holomorphic representation of the Jacobi algebra $\mathfrak{h}_n\rtimes \mathfrak{sp}(n,\R)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}^n\times \mathcal{D}_n$. We construct…

Let $D$ be a strictly pseudoconvex domain in $\C^N$ and $X$ a pure-dimensional non-reduced subvariety that behaves well at $\partial D$. We provide $L^p$-estimates of extensions of holomorphic functions defined on $X$.

In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative…

We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds $M$ of finite volume. Sharp conditions ensuring $L^q(M)$ and $L^\infty (M)$ bounds for eigenfunctions are exhibited in terms of either the isoperimetric…

We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…

We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space, to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect…