Results 151 to 160 of about 7,643 (187)
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Finite sums of dual Toeplitz products
Studia Mathematica, 2021Summary: We consider dual Toeplitz operators acting on the orthogonal complements of two kinds of Dirichlet spaces on the unit ball. We first characterize compactness for operators which are finite sums of dual Toeplitz products. Next, we give a characterization of when a finite sum of products of two dual Toeplitz operators is another dual Toeplitz ...
Y. J. Lee
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Sums of Finite Products of Euler Functions
, 2017In this paper, we consider three types of functions given by sums of finite products of Euler functions and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
Taekyun Kim +3 more
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Finite Sums of Toeplitz Products on the Polydisk
Potential Analysis, 2009The authors study operators \(S\) of the form \[ S=T_\lambda+\sum_{k=1}^N T_{u_k}T_{v_k}, \] where \(u_k, v_k\) are pluriharmonic functions, \(\lambda\) is an \(n\)-harmonic function on the polydisk \(D^n\), and \(T_u f=P(uf)\) is the Toeplitz operator with symbol \(u\) in the Bergman space \(A^2(D^n)\).
B. Choe, H. Koo, Y. J. Lee
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On the Evaluation of Certain Finite Sums of Progressive Products
The Journal of the Royal Aeronautical Society, 1959This note is concerned with the evaluation of the finite sumwhere the m quantities Zi are arbitrary and whereis the binomial coefficient in a series of n terms. Summations of this kind appear in the evaluation of matrix products involving the reciprocal of order n of a segment of a Hilbert matrix or of a generalised Hilbert matrix.
A. R. Collar
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Some representations of sums of finite products of Fibonacci type numbers and polynomials
Journal of Information & Optimization SciencesThis paper will consider a new set of identities expressing sums of finite products of the negative indexed Lucas, Fibonacci, & Complex Fibonacci numbers as a linear combination of Pell polynomials, using their basic properties, through elementary ...
J. Kishore, Vipin Verma
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IDENTITIES FOR PRODUCTS OF GAUSS SUMS OVER FINITE FIELDS
1981Several interesting identities are found and proved for Gauss sums defined over finite fields. With \(\zeta=\exp(2\pi i/p)\), \(p\) a prime, define the Gauss some over \(\mathrm{GF}(p^r)\) \((r\geq 1)\) by \[ G(\chi)=G_r(\chi)=-\sum_{x\in\mathrm{GF}(p^r)} \chi(x)\zeta^{\mathrm{Tr}(x)} \] where \(\mathrm{Tr}\) is the trace map from \(\mathrm{GF}(p^r ...
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Sums and Products from a Finite Set of Real Numbers
The Ramanujan Journal, 1998Let \(A\) be a set of real numbers. Put \(hA=\{x_1+x_2+ \cdots +x_h \mid x_i\in A\}\) and \(A^h=\{x_1x_2 \cdots x_h \;| \;x_i\in A\}\). The author deals with a conjecture of P. Erdős stating that \(hA\cup A^h\) has large cardinality. As observed at the end of the paper, the best results known on this conjecture are due to \textit{G. Elekes} [Acta Arith.
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Indian Journal of Science and Technology
Objective: Classical orthogonal polynomials are extensively used for the numerical solution of differential equations and numerical analysis. Various generalization problems involving Chebyshev polynomials have been studied and one such area is the ...
J. Kishore, Vipin Verma
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Objective: Classical orthogonal polynomials are extensively used for the numerical solution of differential equations and numerical analysis. Various generalization problems involving Chebyshev polynomials have been studied and one such area is the ...
J. Kishore, Vipin Verma
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Sums of Euler products and statistics of elliptic curves
, 2015We present several results related to statistics for elliptic curves over a finite field $$\mathbb {F}_p$$Fp as corollaries of a general theorem about averages of Euler products that we demonstrate. In this general framework, we can reprove known results
Chantal David +2 more
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Finite Graphs and the Number of Sums and Products
1996Let G be a graph with k vertices (1, 2, …, k) and e edges. Let A = (α1,α2,..,α k ) be a set of k integers, and let G(A) be the set of all integers of the form α i + α j and α i α j , where (i,j) is an edge of G. Erdos and Szemeredi conjectured that |G(α)| ≫ e e /k e for every e > 0 and every set A.
Xing-De Jia, Melvyn B. Nathanson
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