7,996 research outputs found
Riesz transforms for Jacobi expansions
We define and study Riesz transforms and conjugate Poisson integrals
associated with multi-dimensional Jacobi expansions.Comment: 24 pages; the paper will appear in J. Anal. Math. (2008
An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems
Numerical solution of the Helmholtz equation in an infinite domain often involves restriction of the domain to a bounded computational window where a numerical solution method is applied. On the boundary of the computational window artificial transparent boundary conditions are posed, for example, widely used perfectly matched layers (PMLs) or absorbing boundary conditions (ABCs). Recently proposed transparent-influx boundary conditions (TIBCs) resolve a number of drawbacks typically attributed to PMLs and ABCs, such as introduction of spurious solutions and the inability to have a tight computational window. Unlike the PMLs or ABCs, the TIBCs lead to a nonlinear dependence of the boundary integral operator on the frequency. Thus, a nonlinear Helmholtz eigenvalue problem arises. \ud
This paper presents an approach for solving such nonlinear eigenproblems which is based on a truncated singular value decomposition (SVD) polynomial approximation of the nonlinearity and subsequent solution of the obtained approximate polynomial eigenproblem with the Jacobi-Davidson method
Weighted norm inequalities for polynomial expansions associated to some measures with mass points
Fourier series in orthogonal polynomials with respect to a measure on
are studied when is a linear combination of a generalized Jacobi
weight and finitely many Dirac deltas in . We prove some weighted norm
inequalities for the partial sum operators , their maximal operator
and the commutator , where denotes the operator of pointwise
multiplication by b \in \BMO. We also prove some norm inequalities for
when is a sum of a Laguerre weight on and a positive mass on
Jost Functions and Jost Solutions for Jacobi Matrices, II. Decay and Analyticity
We present necessary and sufficient conditions on the Jost function for the
corresponding Jacobi parameters and to have a given degree of
exponential decay.Comment: 28 page
Fourth Moment Theorems for Markov Diffusion Generators
Inspired by the insightful article arXiv:1210.7587, we revisit the
Nualart-Peccati-criterion arXiv:math/0503598 (now known as the Fourth Moment
Theorem) from the point of view of spectral theory of general Markov diffusion
generators. We are not only able to drastically simplify all of its previous
proofs, but also to provide new settings of diffusive generators (Laguerre,
Jacobi) where such a criterion holds. Convergence towards gamma and beta
distributions under moment conditions is also discussed.Comment: 15 page
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