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On the Computation of Fourier Coefficients
"... In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f ′ (t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f ′ (t) are known, and vice ver ..."
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In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f ′ (t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f ′ (t) are known, and vice
AN UPDATE ALGORITHM FOR FOURIER COEFFICIENTS
"... In this article we present a new technique to obtain the Discrete Fourier coefficients for a moving data window of an arbitrary length. Unlike the classic approaches we derive an update algorithm by exploiting results of update formulas for orthogonal polynomials. For the vector space of polynomial ..."
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In this article we present a new technique to obtain the Discrete Fourier coefficients for a moving data window of an arbitrary length. Unlike the classic approaches we derive an update algorithm by exploiting results of update formulas for orthogonal polynomials. For the vector space
Quadrature formulae for Fourier coefficients
, 2009
"... We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the FourierTchebycheff coefficients given b ..."
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We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the FourierTchebycheff coefficients given
Fourier Coefficients for G_2
, 1999
"... this paper, we develop a theory of Fourier coefficients c A (f) for certain modular forms f on the split group G 2 over Q. The coefficients are indexed by totally real cubic rings A: commutative rings with unit that are free of rank 3 over Z, such that the Ralgebra ..."
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this paper, we develop a theory of Fourier coefficients c A (f) for certain modular forms f on the split group G 2 over Q. The coefficients are indexed by totally real cubic rings A: commutative rings with unit that are free of rank 3 over Z, such that the Ralgebra
ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF
"... Abstract: We prove a formula relating the Fourier coefficients of a modular form of halfintegral weight to the special values of Lfunctions. The form in question is an explicit theta lift from the multiplicative group of an indefinite quaternion algebra over Q. This formula has applications to pro ..."
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Abstract: We prove a formula relating the Fourier coefficients of a modular form of halfintegral weight to the special values of Lfunctions. The form in question is an explicit theta lift from the multiplicative group of an indefinite quaternion algebra over Q. This formula has applications
On the Fourier coefficients of homeomorphisms of the circle
, 1998
"... I. Introduction. Let f(eis) be a sense preserving homeomorphism of the unit circle. In order to study the Fourier coecients of f, we consider 2periodic functions ei!(s) formed with nondecreasing!(s), and the Fourier series (1.1) ei!(s) ..."
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Cited by 3 (0 self)
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I. Introduction. Let f(eis) be a sense preserving homeomorphism of the unit circle. In order to study the Fourier coecients of f, we consider 2periodic functions ei!(s) formed with nondecreasing!(s), and the Fourier series (1.1) ei!(s)
On signs of Fourier coefficients of cusp forms
, 2012
"... We consider two problems concerning signs of Fourier coefficients of classical modular forms, or equivalently Hecke eigenvalues: first, we give an upper bound for the size of the first signchange of Hecke eigenvalues in terms of conductor and weight; second, we investigate to what extent the signs ..."
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Cited by 6 (1 self)
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We consider two problems concerning signs of Fourier coefficients of classical modular forms, or equivalently Hecke eigenvalues: first, we give an upper bound for the size of the first signchange of Hecke eigenvalues in terms of conductor and weight; second, we investigate to what extent the signs
ESTIMATES OF FOURIER COEFFICIENTS
"... Abstract. Some wellknown properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems. ..."
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Abstract. Some wellknown properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems.
Results 1  10
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228,133