随机 ntz多项式的零

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI:10.1016/j.jmaa.2025.129799

Doron S. Lubinsky , Igor E. Pritsker

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引用次数: 0

摘要

研究了具有实数iid系数的m ntz多项式的正零期望值。对于标准高斯系数，当跨越随机m ntz多项式的m ntz单项式的指数具有多项式和对数增长时，我们建立了期望的正零数的渐近结果。我们还给出了具有各种实数i - id系数的随机m ntz多项式的期望零点数的许多边界，包括任意非平凡实数i - id系数的情况。由于m ntz多项式包括空白多项式，稀疏多项式或作为特殊情况的少多项式，我们的结果直接适用于那些具有间隙的多项式类的实零的期望数。

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Zeros of random Müntz polynomials

We study the expected number of positive zeros of Müntz polynomials with real i.i.d. coefficients. For the standard Gaussian coefficients, we establish asymptotic results for the expected number of positive zeros when the exponents of Müntz monomials that span our random Müntz polynomials have polynomial and logarithmic growth. We also present many bounds on the expected number of zeros of random Müntz polynomials with various real i.i.d. coefficients, including the case of arbitrary nontrivial real i.i.d. coefficients. Since Müntz polynomials include lacunary polynomials, sparse polynomials or fewnomials as special cases, our results directly apply to the expected number of real zeros for those classes of polynomials with gaps.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.