Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Rezola M"'
Autor:
Peña, A., Rezola, M. L.
We study the inverse problem in the theory of (standard) orthogonal polynomials involving two polynomials families $(P_n)_n$ and $(Q_n)_n$ which are connected by a linear algebraic structure such as $$P_n(x)+\sum_{i=1}^N r_{i,n}P_{n-i}(x)=Q_n(x)+\sum
Externí odkaz:
http://arxiv.org/abs/1810.01691
Autor:
Peña, A., Rezola, M. L.
In this paper the discrete Sobolev inner product $$< p,q > =\int p(x) q(x) \,d\mu + \sum_{i=0}^r M_i \, p^{(i)}(c) \, q^{(i)}(c)$$ is considered, where $\mu$ is a finite positive Borel measure supported on an infinite subset of the real line, $c\in\m
Externí odkaz:
http://arxiv.org/abs/1411.3120
Let $\{\mathbb{P}_n\}_{n\ge 0}$ and $\{\mathbb{Q}_n\}_{n\ge 0}$ be two monic polynomial systems in several variables satisfying the linear structure relation $$\mathbb{Q}_n = \mathbb{P}_n + M_n \mathbb{P}_{n-1}, \quad n\ge 1,$$ where $M_n$ are consta
Externí odkaz:
http://arxiv.org/abs/1307.5999
Let $(P_n)_n$ and $(Q_n)_n$ be two sequences of monic polynomials linked by a type structure relation such as $$ Q_{n}(x)+r_nQ_{n-1}(x)=P_{n}(x)+s_nP_{n-1}(x)+t_nP_{n-2}(x)\;, $$ where $(r_n)_n$, $(s_n)_n$ and $(t_n)_n$ are sequences of complex numbe
Externí odkaz:
http://arxiv.org/abs/1212.4271
Autor:
Peña, A., Rezola, M. L.
C. Markett proved a Cohen type inequality for the classical Laguerre expansions in the appropriate weighted $L^{p}$ spaces. In this paper, we get a Cohen type inequality for the Fourier expansions in terms of discrete Laguerre--Sobolev orthonormal po
Externí odkaz:
http://arxiv.org/abs/1107.0832
In this paper we deal with polynomials orthogonal with respect to an inner product involving derivatives, that is, a Sobolev inner product. Indeed, we consider Sobolev type polynomials which are orthogonal with respect to $$(f,g)=\int fg d\mu +\sum_{
Externí odkaz:
http://arxiv.org/abs/1003.3336
Let $\{P_n \}_{n\ge0}$ be a sequence of monic orthogonal polynomials with respect to a quasi--definite linear functional $u$ and $\{Q_n \}_{n\ge0}$ a sequence of polynomials defined by $$Q_n(x)=P_n(x)+s_n P_{n-1}(x)+t_n P_{n-2}(x),\quad n\ge1,$$ with
Externí odkaz:
http://arxiv.org/abs/0909.0619
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties.
Externí odkaz:
http://arxiv.org/abs/0909.0617
When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
Given $\{P_n \}$ a sequence of monic orthogonal polynomials, we analyze their linear combinations $\{Q_n \}$with constant coefficients and fixed length $k+1$. Necessary and sufficient conditions are given for the orthogonality of the monic sequence $
Externí odkaz:
http://arxiv.org/abs/0711.1740
Let $\mu_0$ and $\mu_1$ be measures supported on an unbounded interval and $S_{n,\lambda_n}$ the extremal varying Sobolev polynomial which minimizes \begin{equation*} < P, P >_{\lambda_n}=\int P^2 d\mu_0 + \lambda_n \int P'^2 d\mu_1, \quad \lambda_n
Externí odkaz:
http://arxiv.org/abs/math/0606589