scholarly journals Asymptotic distribution of zeros of polynomials satisfying difference equations

2003 ◽  
Vol 150 (1) ◽  
pp. 57-70 ◽  
Author(s):  
I.V. Krasovsky
Keyword(s):  
Asymptotic Distribution ◽  
Difference Equations ◽  
Zeros Of Polynomials ◽  
Distribution Of Zeros ◽  
Asymptotic Distribution Of Zeros

scholarly journals Polynomials of Least Deviation from Zero in Sobolev p-Norm

2022 ◽  
Author(s):  
Abel Díaz-González ◽  
Héctor Pijeira-Cabrera ◽  
Javier Quintero-Roba
Keyword(s):  
Convex Hull ◽  
Asymptotic Distribution ◽  
Zeros Of Polynomials ◽  
Order Restriction ◽  
Distribution Of Zeros ◽  
Location Of Zeros ◽  
Discrete Part ◽  
Asymptotic Distribution Of Zeros ◽  
General Conditions

AbstractThe first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm ($$1<p<\infty $$ 1 < p < ∞ ) for the case $$p=1$$ p = 1 . Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev p-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that the n-th polynomial of least deviation has at least $$n-\mathbf {d}^*$$ n - d ∗ zeros on the convex hull of the support of the measure, where $$\mathbf {d}^*$$ d ∗ denotes the number of terms in the discrete part.

scholarly journals CONVERGENCE OF FUBINI–STUDY CURRENTS FOR ORBIFOLD LINE BUNDLES

2013 ◽  
Vol 24 (07) ◽  
pp. 1350051 ◽  
Author(s):  
DAN COMAN ◽  
GEORGE MARINESCU
Keyword(s):  
Line Bundle ◽  
Asymptotic Distribution ◽  
Line Bundles ◽  
Singular Line ◽  
Distribution Of Zeros ◽  
Bergman Kernels ◽  
Holomorphic Sections ◽  
Asymptotic Distribution Of Zeros

We discuss positive closed currents and Fubini–Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini–Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.

scholarly journals On the Distribution of Zeros and Poles of Rational Approximants on Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
V. V. Andrievskii ◽  
H.-P. Blatt ◽  
R. K. Kovacheva
Keyword(s):  
Asymptotic Distribution ◽  
Polynomial Approximation ◽  
Additional Assumption ◽  
Equilibrium Measure ◽  
Distribution Of Zeros ◽  
Rational Approximants ◽  
Bounded Degree ◽  
Asymptotic Distribution Of Zeros ◽  
Best Rational Approximants ◽  
Zeros And Poles

The distribution of zeros and poles of best rational approximants is well understood for the functions , . If is not holomorphic on , the distribution of the zeros of best rational approximants is governed by the equilibrium measure of under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, -values, and poles of best real rational approximants of degree at most to a function that is real-valued, but not holomorphic on . Generalizations to the lower half of the Walsh table are indicated.

Note on the distribution of zeros of polynomials

1969 ◽  
Vol 5 (6) ◽  
pp. 444-445
Author(s):  
V. A. Baranova
Keyword(s):  
Zeros Of Polynomials ◽  
Distribution Of Zeros

scholarly journals Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 258 ◽  
Author(s):  
Subuhi Khan ◽  
Tabinda Nahid
Keyword(s):  
Generating Function ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Computer Experiment ◽  
Appell Polynomials ◽  
Distribution Of Zeros ◽  
Hybrid Form ◽  
Special Polynomials

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

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