Extremal problems, inequalities, and classical orthogonal polynomials

نویسندگان

  • Ravi P. Agarwal
  • Gradimir V. Milovanovic
چکیده

In this survey paper we give a short account on characterizations for very classical orthogonal polynomials via extremal problems and the corresponding inequalities. Beside the basic properties of the classical orthogonal polynomials we consider polynomial inequalities of Landau and Kolmogoroff type, some weighted polynomial inequalities in L2-norm of Markov-Bernstein type, as well as the corresponding connections with the classical orthogonal polynomials.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Orthogonal Polynomials and Quadratic Extremal Problems

The purpose of this paper is to analyse a class of quadratic extremal problems defined on various Hilbert spaces of analytic functions, thereby generalizing an extremal problem on the Dirichlet space which was solved by S.D. Fisher. Each extremal problem considered here is shown to be connected with a system of orthogonal polynomials. The orthogonal polynomials then determine properties of the ...

متن کامل

Products of Polynomials in Uniform Norms

We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. This subject includes the well known Gel’fond-Mahler inequalities for the unit disk and Kneser inequality for the segment [−1, 1]. Using tools of complex analysis and potential theory, we prove a sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set ...

متن کامل

Topics in polynomials - extremal problems, inequalities, zeros

Where you can find the topics in polynomials extremal problems inequalities zeros easily? Is it in the book store? On-line book store? are you sure? Keep in mind that you will find the book in this site. This book is very referred for you because it gives not only the experience but also lesson. The lessons are very valuable to serve for you, that's not about who are reading this topics in poly...

متن کامل

Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems

We investigate monotonicity properties of extremal zeros of orthogonal polynomials depending on a parameter. Using a functional analysis method we prove the monotonicity of extreme zeros of associated Jacobi, associated Gegenbauer and q-Meixner-Pollaczek polynomials. We show how these results can be applied to prove interlacing of zeros of orthogonal polynomials with shifted parameters and to d...

متن کامل

Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well-known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial pn(x) interlace with the zeros of pn(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of k-th, 1 ≤ k ≤ n − 1, zeros of the associated polynomial and the derivative of an orthogonal...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Applied Mathematics and Computation

دوره 128  شماره 

صفحات  -

تاریخ انتشار 2002