Related papers: The Pad\'e interpolation method applied to $q$-Pai…
We investigate the connection problem for the Jackson integral of type $A_n$. Our connection formula implies a Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific multiple…
It is possible to generalize the fruitful interaction between (real or complex) Jacobi matrices, orthogonal polynomials and Pade approximants at infinity by considering rational interpolants, (bi-)orthogonal rational functions and linear…
Let $p,q$ be functions on $\mathbb{R}^{N}$ satisfying $1\ll q\ll p\ll N$, we consider $p(x)$-Laplacian problems of the form \[ \left\{ \begin{array} [c]{l}% -\Delta_{p(x)}u+V(x)\vert u\vert ^{p(x)-2}u=\lambda\vert u\vert…
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are…
One strategy to solve a nonlinear eigenvalue problem $T(\lambda)x=0$ is to solve a polynomial eigenvalue problem (PEP) $P(\lambda)x=0$ that approximates the original problem through interpolation. Then, this PEP is usually solved by…
Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.
We present here a new splitting method to solve Lyapunov equations of the type $AP + PA^T=-BB^T$ in a Kronecker product form. Although that resulting matrix is of order $n^2$, each iteration of the method demands only two operations with…
We study the problem of $P$-interpolation, where $P$ is a set of binary predicate symbols, for certain classes of local extensions of a base theory. For computing the $P$-interpolating terms, we use a hierarchic approach: This allows us to…
We use $L^2$ estimates for the $\bar\partial$ equation to find geometric conditions on discrete interpolating varieties for weighted spaces $A_p(\C)$ of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$. In particular, we…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
We treat the interpolation problem $ \{f(x_j)=y_j\}_{j=1}^N $ for polynomial and rational functions. Developing the approach by C.Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences $…
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in \cite{LSX}. The main results consist of a new derivation of the Gaussian type cubature for the…
We show how the newly developed method of Periodic Unfolding on Riemannian manifolds can be applied to PDE problems: We consider the homogenization of an elliptic model problem. In the limit, we obtain a generalization of the well-known…
We present an asymmetric $q$-Painlev\'e equation. We will derive this using $q$-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this $q$-Painlev\'e equation (up to a simple…
We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin spaces. An…
We describe a method to construct well-posed initial value problems for not necessarily integrable equations on not necessarily simply connected quad-graphs. Although the method does not always provide a well-posed initial value problem…
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…
We present new Pieri type formulas for Jack polynomials. As an application, we give a new derivation of higher order difference equations for interpolation Jack polynomials originally found by Knop and Sahi. We also propose Pieri formulas…
A popular robust alternative of the classic principal component analysis (PCA) is the $\ell_1$-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the $\ell_1$-norm. L1-PCA has shown…