On orthogonal polynomials with positive zeros and the associated kernel polynomials
نویسندگان
چکیده
منابع مشابه
On Orthogonal Polynomials with Regularly Distributed Zeros
In this case the points 0k,, = are sin xkn are equidistributed in Weyl's sense . A non-negative measure da for which the array xkn (da) has the distribution function fl o(t) will be called an arc-sine measure . If du(x) = w(x) dx is absolutely continuous, we apply, replacing dca by w, the notations pn(W,x), yn (w), xkn(w) and call a non-negative w(x) an arc-sine weight if da(x) = w(x) dx is an ...
متن کاملWeighted sums of orthogonal polynomials with positive zeros
We study the two sequences of polynomials which arise as denominators of the approximants of even and odd order, respectively, of a Stieltjes fraction, and which may be defined alternatively as a sequence of orthogonal polynomials with positive zeros and the associated sequence of kernel polynomials. Motivated by problems in the setting of birth-death processes, where these sequences play a maj...
متن کاملLocating Zeros of Polynomials Associated With Daubechies Orthogonal Wavelets
In the last decade, Daubechies orthogonal wavelets have been successfully used and proved their practicality in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. I...
متن کاملZeros of Polynomials Orthogonal on Several Intervals
Let a1 < a2 < . . . < a2l, Ej = [a2j−1, a2j ], put E = ⋃l j=1 Ej and H(x) = ∏2l j=1(x − aj). Furthermore let pn(x) = x + . . . be the polynomial of degree n orthogonal on E with respect to a weight function of the form w/ √ −H with square root singularities at the boundary points of E and w ∈ C(E). We study and answer the following questions: how many zeros has pn in the interval Ej , j ∈ {1, ....
متن کاملOn extreme zeros of classical orthogonal polynomials
Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision,...
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: Journal of Mathematical Analysis and Applications
سال: 1986
ISSN: 0022-247X
DOI: 10.1016/0022-247x(86)90315-x