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607
Some extremal functions in Fourier analysis, II
, 2008
"... We obtain extremal majorants and minorants of exponential type for a class of even functions on R which includes log x  and x  α, where −1 < α < 1. We also give periodic versions of these results in which the majorants and minorants are trigonometric polynomials of bounded degree. As appl ..."
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Cited by 88 (10 self)
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. As applications we obtain optimal estimates for certain Hermitian forms, which include discrete analogues of the one dimensional HardyLittlewoodSobolev inequalities. A further application provides an ErdösTurántype inequality that estimates the sup norm of algebraic polynomials on the unit disc in terms
BOUNDS FOR DEGREES AND SUMS OF DEGREES OF IRREDUCIBLE CHARACTERS OF SOME CLASSICAL GROUPS OVER FINITE FIELDS
"... The goal of this note (which is incorporated and expanded in Chapter 5 of the author’s book “The large sieve and its applications ” ) is to bound from above in a suitable manner the degree of irreducible representations, and the sum of the degrees of irreducible representations, of a group Gℓ, which ..."
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The goal of this note (which is incorporated and expanded in Chapter 5 of the author’s book “The large sieve and its applications ” ) is to bound from above in a suitable manner the degree of irreducible representations, and the sum of the degrees of irreducible representations, of a group Gℓ
A Gaussian Sum Approach to Phase and Frequency Estimation
"... Abstract–In this paper, a theory of optimaf nonlinear estimation from sampIed data signals where the a posterion probability densities are approximated by Gaussian sums is adapted for application to phase and frequency estimation in high noise. The nonlinear estimators (demodulators) require paralle ..."
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Abstract–In this paper, a theory of optimaf nonlinear estimation from sampIed data signals where the a posterion probability densities are approximated by Gaussian sums is adapted for application to phase and frequency estimation in high noise. The nonlinear estimators (demodulators) require
Vinogradov's Method and Some Applications
, 1996
"... In this talk we consider in an elementary way some simple problems which relate to incomplete sums and can be studied by appealing to a classical method of Vinogradov and its modifications. Vinogradov's idea was to use finite Fourier transforms in order to estimate an incomplete sum by means of ..."
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Cited by 1 (0 self)
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of complete but in some respects more complicated sums. A natural application was to estimate an incomplete sum of multiplicative characters by means of Gaussian sums. This application can be generalized in many natural ways; e.g., we may find bounds for the least nonnegative residue or nonresidue of a
ClosedLoop Applicability of the SignPerturbed Sums Method
"... Abstract — SignPerturbed Sums (SPS) is a nonasymptotic system identification method that can construct confidence regions for general linear systems. It works under mild statistical assumptions, such as symmetric and independent noise terms. The SPS confidence region includes the prediction error ..."
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error estimate (PEM) and, for any finite sample and userchosen confidence probability, it contains the true system parameter with exactly the given probability. Originally, SPS was introduced for openloop systems, this paper overviews its applicability in closedloop setups. The three main PEM
Lfunctions for symmetric products of Kloosterman sums
 J. Reine Angew. Math
"... The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and ∞. We study the local monodromy of this representation at ∞ using ladic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of ..."
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Cited by 22 (12 self)
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The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and ∞. We study the local monodromy of this representation at ∞ using ladic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors
Diophantine Methods for Exponential Sums, and Exponential Sums for Diophantine Problems
, 2003
"... Recent developments in the theory and application of the HardyLittlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential sums are described first, concentrating on developme ..."
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Cited by 1 (1 self)
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Recent developments in the theory and application of the HardyLittlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential sums are described first, concentrating
NonStandard Behavior of Density Estimators for Sums of Squared Observations”.
 Statist. Decisions
, 2009
"... Abstract. Densities of functions of two or more independent random variables can be estimated by local Ustatistics. 1. The density estimator of a sum of squares of independent observations typically slows down by a logarithmic factor. For exponents greater than two, the estimator behaves like a c ..."
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Cited by 4 (4 self)
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Abstract. Densities of functions of two or more independent random variables can be estimated by local Ustatistics. 1. The density estimator of a sum of squares of independent observations typically slows down by a logarithmic factor. For exponents greater than two, the estimator behaves like a
Results 11  20
of
607