Orthogonality on the semicircle: old and new results
نویسندگان
چکیده
Orthogonal polynomials on the semicircle were introduced by Gautschi and MilovanoviÄ in [Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (July 1985), pp. 179-185] [J. Approx. Theory, 46 (1986), 230-250]. In this paper we give an account of kind orthogonality, weighted generalizations mainly oriented to Chebyshev weights first second kinds, including several interesting properties such polynomials. Moreover, also present a number new results those for Laurent (rational functions) orthogonal semicircle. particular, their recurrence relations study special cases Legendre weight kind. Explicit expressions systems with are presented, as well corresponding zero distributions.
منابع مشابه
on the comparison of keyword and semantic-context methods of learning new vocabulary meaning
the rationale behind the present study is that particular learning strategies produce more effective results when applied together. the present study tried to investigate the efficiency of the semantic-context strategy alone with a technique called, keyword method. to clarify the point, the current study seeked to find answer to the following question: are the keyword and semantic-context metho...
15 صفحه اولOld and New Results on theTwo - Dimensional
This paper deals with linear and non-linear hydrodynamic stability of the two-dimensional Poiseuille ow. A new numerical approach for the study of linear stability is presented. A numerical study of the transition of the ow to chaos is also presented. Using tools from dynamical system theory, we identify and characterize the di erent solutions of the Navier-Stokes equations at di erent values o...
متن کاملOld and New Results on Snas on the Real Line
Classical and new results concerning the topological structure of skew-products semiflows, coming from non-autonomous maps and differential equations, are combined in order to establish rigorous conditions giving rise to the occurrence of strange nonchaotic attractors. A special attention is paid to the relation of these sets with the almost automorphic extensions of the base flow. The scope of...
متن کاملPolynomials Orthogonal on the Semicircle
In the above two papers Walter Gautschi, jointly with Henry J. Landau and Gradimir V. Milovanović, investigate polynomials that are orthogonal with respect to a non-Hermitian inner product defined on the upper half of the unit circle in the complex plane. For special choices of the weight function, these polynomials are related to Jacobi polynomials. Their recurrence relation and properties of ...
متن کاملNew results on the quasi-commuting inverses
A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, inother words, if its columns (or rows) are linearly independent. In recent years needs have been felt innumerous areas of applied mathematics for some kind of partial inverse of a matrix that is singularor even rectangular. In this paper, some results on the Quasi-commuting inverses, are given an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Transactions on Numerical Analysis
سال: 2023
ISSN: ['1068-9613', '1097-4067']
DOI: https://doi.org/10.1553/etna_vol59s99