scholarly journals Rademacher-Gaussian tail comparison for complex coefficients and related problems

2021 ◽  
pp. 1
Author(s):  
Giorgos Chasapis ◽  
Ruoyuan Liu ◽  
Tomasz Tkocz
Keyword(s):  
Complex Coefficients

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

A class of symmetric ordinary differential operators whose deficiency numbers differ by an integer†

1978 ◽  
Vol 82 (1-2) ◽  
pp. 117-134 ◽  
Author(s):  
Richard C. Gilbert
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Asymptotic Expansions ◽  
Differential Operators ◽  
Ordinary Differential Operator ◽  
Ordinary Differential Operators ◽  
Half Axis ◽  
Complex Coefficients

SynopsisFormulas are determined for the deficiency numbers of a formally symmetric ordinary differential operator with complex coefficients which have asymptotic expansions of a prescribed type on a half-axis. An implication of these formulas is that for any given positive integer there exists a formally symmetric ordinary differential operator whose deficiency numbers differ by that positive integer.

Estimates of Zeros of a Polynomial

1962 ◽  
Vol 58 (2) ◽  
pp. 229-234 ◽  
Author(s):  
L. Mirsky
Keyword(s):  
Integral Formula ◽  
Transcendental Numbers ◽  
Image Position ◽  
Complex Coefficients

Throughout this note we shall consider a fixed polynomial with complex coefficients and of degree n ≥ 2. Its zeros will be denoted by ξ1, ξ2, …, ξn where the numbering is such that Making use of Jensen's integral formula, Mahler (4) showed that, for l ≥ k < n, A slightly weaker result had been established by Feldman in an earlier publication (2). Mahler's inequality (1) is of importance in the study of transcendental numbers, and our first object is to sharpen his bound by proving the following result.

scholarly journals Free non-associative principal train algebras

1984 ◽  
Vol 27 (3) ◽  
pp. 313-319 ◽  
Author(s):  
P. Holgate
Keyword(s):  
Finite Number ◽  
Ground Field ◽  
Linear Forms ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Senses ◽  
Special Train ◽  
Complex Coefficients ◽  
Infinite Linear

The definitions of finite dimensional baric, train, and special train algebras, and of genetic algebras in the senses of Schafer and Gonshor (which coincide when the ground field is algebraically closed, and which I call special triangular) are given in Worz-Busekros's monograph [8]. In [6] I introduced applications requiring infinite dimensional generalisations. The elements of these algebras were infinite linear forms in basis elements a0, a1,… and complex coefficients such that In this paper I consider only algebras whose elements are forms which only a finite number of the xi are non zero.

scholarly journals New Soliton Solutions of the (2+1)-Dimensional System Davey-Stewartson Equation

2018 ◽  
Vol 7 (4.1) ◽  
pp. 37 ◽  
Author(s):  
Anwar J Ja'afar Mohamad Jawad ◽  
Mahmood J. Abu-Al Shaeer ◽  
Marko D. Petkovi_c
Keyword(s):  
Soliton Solutions ◽  
Travelling Wave ◽  
Simple Equation ◽  
Equation Method ◽  
Initial System ◽  
Wave Transformation ◽  
Dimensional System ◽  
Modified Simple Equation Method ◽  
Complex Coefficients

In this paper, we derive several soliton solutions of the generalized Davey-Stewartson equation with the complex coefficients. First we use the travelling wave transformation to reduce the initial system to ODE. The equivalent ODE is then solved, giving several classes of solutions, depending on the values of the parameters. Finally, the Extended Tanh-Coth method and Modified simple equation method.  

scholarly journals The reduced length of a polynomial with complex coefficients

2008 ◽  
Vol 133 (1) ◽  
pp. 73-81 ◽  
Author(s):  
A. Schinzel
Keyword(s):  
Complex Coefficients

scholarly journals Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bing Xu ◽  
Janusz Brzdęk
Keyword(s):  
Ulam Stability ◽  
Linear Difference Equations ◽  
Positive Real ◽  
Fixed Sequence ◽  
Linear Recurrences ◽  
Order Linear ◽  
First Order ◽  
Constant Coefficients ◽  
Complex Coefficients ◽  
Positive Real Constant

We study the Hyers-Ulam stability in a Banach spaceXof the system of first order linear difference equations of the formxn+1=Axn+dnforn∈N0(nonnegative integers), whereAis a givenr×rmatrix with real or complex coefficients, respectively, and(dn)n∈N0is a fixed sequence inXr. That is, we investigate the sequences(yn)n∈N0inXrsuch thatδ∶=supn∈N0yn+1-Ayn-dn<∞(with the maximum norm inXr) and show that, in the case where all the eigenvalues ofAare not of modulus 1, there is a positive real constantc(dependent only onA) such that, for each such a sequence(yn)n∈N0, there is a solution(xn)n∈N0of the system withsupn∈N0yn-xn≤cδ.

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