Results 1 to 10 of about 1,059,315 (385)
Surveys in Approximation Theory, 1 (2005), 70-125, 2005 In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
T. Koornwinder +3 more
arxiv +5 more sources
Krylov complexity and orthogonal polynomials [PDF]
Nuclear Physics B, 2022 Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method.
Wolfgang Mück, Yi Yang
doaj +2 more sources
Asymptotics of skew orthogonal polynomials [PDF]
J. Phys. A. 34 2001 7591-7605, 2000 Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials of random matrices. From there, asymptotics of the skew orthogonal polynomials are derived.
B Eynard +13 more
arxiv +3 more sources
Upward extension of the Jacobi matrix for orthogonal polynomials [PDF]
arXiv, 1995 Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix $r$ new rows and columns, so that the original
Ronveaux, André, Van Assche, Walter
arxiv +5 more sources
Coherent Orthogonal Polynomials [PDF]
Annals of Physics, 2012 We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects.
Cambanis +9 more
core +3 more sources
On Sobolev orthogonal polynomials [PDF]
Expositiones Mathematicae, 2014 Sobolev orthogonal polynomials have been studied extensively in the past 20 years. The research in this field has sprawled into several directions and generates a plethora of publications. This paper contains a survey of the main developments up to now.
F. Marcellán, Yuan Xu
semanticscholar +5 more sources
A connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line [PDF]
, 2002 Szego's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials L, and leads to a new orthogonality structure in the module LxL.
Alfaro +22 more
arxiv +4 more sources
Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials [PDF]
SIGMA 19 (2023), 020, 18 pages, 2022 A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are ...
Berezin, Sergey +2 more
arxiv +4 more sources
On Orthogonal Polynomials [PDF]
Transactions of the American Mathematical Society, 1931 J. Geronimus
openalex +3 more sources
The Condition of Orthogonal Polynomials [PDF]
Mathematics of Computation, 1972 An estimate is given for the condition number of the coordinate map associating to each polynomial its coefficients with respect to a system of orthogonal polynomials.
Walter Gautschi
openalex +3 more sources