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412
BIVARIATE DELTA-EVOLUTION EQUATIONS AND CONVOLUTION POLYNOMIALS: COMPUTING POLYNOMIAL EXPANSIONS OF SOLUTIONS.
"... Abstract. This paper describes an application of Rota and collaborator’s ideas on the foundations on combinatorial theory to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials as the entri ..."
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as the entries, in the matrix representation, of the exponentials of certain contractive linear operators in the ring of formal power series. This is the starting point to get symbolic solutions to some functional-partial differen-tial equations. We introduce the bivariate convolution product of convolution
Expansion and Poisson Summation Formula for the Series Approximation of the Exponential Function
, 2012
"... ar ..."
REPRESENTATION OF MEAN-PERIODIC FUNCTIONS IN SERIES OF EXPONENTIAL POLYNOMIALS
, 803
"... ABSTRACT. Let θ be a Young function and consider the space Fθ(C) of all entire functions with θ-exponential growth. In this paper, we are interested in the solutions f ∈ Fθ(C) of the convolution equation T ⋆ f = 0, called mean-periodic functions, where T is in the topological dual of Fθ(C). We show ..."
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ABSTRACT. Let θ be a Young function and consider the space Fθ(C) of all entire functions with θ-exponential growth. In this paper, we are interested in the solutions f ∈ Fθ(C) of the convolution equation T ⋆ f = 0, called mean-periodic functions, where T is in the topological dual of Fθ(C). We show
On the approximation of square-integrable functions by exponential series
"... ABSTRACT The expansion of a real square-integrable function in a Legendre series is considered. Existence of best approximations from different sets of exponential functions and their mean convergence to the function in question are proved. As an extension of this result existence and mean converge ..."
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ABSTRACT The expansion of a real square-integrable function in a Legendre series is considered. Existence of best approximations from different sets of exponential functions and their mean convergence to the function in question are proved. As an extension of this result existence and mean
Generalized Exponential Euler Polynomials and Exponential Splines
, 2011
"... Abstract Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applic ..."
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. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.
Chapel Hill, North CarolinaCHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION BY RELEVATION TYPE EQUATIONS By
, 1979
"... In this note two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. These results were motivated by the notion of "relevation of distributions" introduced by Krakowski (1973). Key words: exponential distribution; chara ..."
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; characterization; relevation; convolution; power series expansion; Laplace transform; non-negative random variables; replacenent procedures.
A novel pricing method for European options based on Fourier-cosine series expansions
- SIAM J. SCI. COMPUT
, 2008
"... Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, ..."
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Cited by 57 (14 self)
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Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases
Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions
- Numerische Mathematik
"... We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C ∞ [a, b] ∈ R) transitional pr ..."
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Cited by 28 (8 self)
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We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C ∞ [a, b] ∈ R) transitional
Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics
, 1999
"... Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological, is constructed for the corresponding Borel functions. Its main property is ..."
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by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator. PACS number(s): 03.65.-W, 03.65.Sq, 02.30.Lt, 02.30.Mv
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