Zobrazeno 1 - 10
of 68
pro vyhledávání: '"33C47, 42C05"'
Autor:
Huertas, Edmundo J., Mañas, Manuel
Mixed orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss--Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multi
Externí odkaz:
http://arxiv.org/abs/2411.10834
Exceptional extensions of a class of Laurent biorthogonal polynomials (the so-called Hendriksen-van Rossum polynomials) have been presented by the authors recently. This is achieved through Darboux transformations of generalized eigenvalue problems.
Externí odkaz:
http://arxiv.org/abs/2402.06197
For a general number $p\geq 2$ of measures, we provide explicit expressions for the Jacobi-Pi\~neiro and Laguerre of the first kind multiple orthogonal polynomials of type I, presented in terms of multiple hypergeometric functions.
Externí odkaz:
http://arxiv.org/abs/2310.18294
Autor:
Gao, Jing, Iserles, Arieh
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example is integral
Externí odkaz:
http://arxiv.org/abs/2308.08266
Autor:
Cantero, María José, Iserles, Arieh
We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure $z^{\omega-1}\mathrm{d} z$, where $\omega\in\mathbb{R}\setminus\{0\}$. We derive their explicit form, a generating function and several recurrence relati
Externí odkaz:
http://arxiv.org/abs/2308.06059
Autor:
Luo, Yu, Tsujimoto, Satoshi
A formulation is given for the spectral transformation of the generalized eigenvalue problem through the decomposition of the second-order differential operators. This allows us to construct some Laurent biorthogonal polynomial systems with gaps in t
Externí odkaz:
http://arxiv.org/abs/2212.12429
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential relations that t
Externí odkaz:
http://arxiv.org/abs/2209.15372
Autor:
Miki, Hiroshi
Particular class of skew orthogonal polynomials are introduced and investigated, which possess Laurent symmetry. They are also shown to appear as eigenfunctions of symplectic generalized eigenvalue problems. The modification of these polynomials give
Externí odkaz:
http://arxiv.org/abs/2004.13906
Autor:
Horváth, Á. P.
Below the normalized weighted reciprocal of the Christoffel function with respect to exceptional Jacobi polynomials is investigated. It is proved that it tends to the equilibrium measure of the interval of orthogonality in weak-star sense. The main t
Externí odkaz:
http://arxiv.org/abs/2003.11861
Publikováno v:
Results in Mathematics 74 (4) (2019), Art. 144, 12 pp
We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure with support on the real line (Jacobi,
Externí odkaz:
http://arxiv.org/abs/1907.13226