Bernstein–Szegő polynomials on the triangle

نویسنده

  • A. M. Delgado
چکیده

In this work we consider the extension of the one variable Bernstein–Szegő theory for orthogonal polynomials on the real line (see [3]) to bivariate measures supported on the triangle. A similar problem for measures supported in the square was studied in [1]. Following essentially [2] the orthogonal polynomials and the corresponding kernel functions are constructed. Finally, some asymptotic results concerning the Christoffel functions are obtained.

برای دانلود رایگان 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

On a Two Variable Class of Bernstein-szegő Measures

The one variable Bernstein-Szegő theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.

متن کامل

A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

متن کامل

Numerical solution of the spread of infectious diseases mathematical model based on shifted Bernstein polynomials

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

متن کامل

A numerical study of electrohydrodynamic flow analysis in a circular cylindrical conduit using orthonormal Bernstein polynomials

In this work, the nonlinear boundary value problem in electrohydrodynamics flow of a fluid in an ion-drag configuration in a circular cylindrical conduit is studied numerically. An effective collocation method, which is based on orthonormal Bernstein polynomials is employed to simulate the solution of this model. Some properties of orthonormal Bernstein polynomials are introduced and utilized t...

متن کامل

The Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials

‎In this paper‎, ‎we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays‎. ‎Constant or pantograph delays may appear in state-control or both‎. ‎We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then‎, ‎these are utilized to reduce the solution of optimal control with constant...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011