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81.
《Applied and Computational Harmonic Analysis》2014,36(1):158-166
Gabor functions, Gaussian wave packets, are optimally localized in time and frequency, and thus in principle ideal as (frame) basis functions for a wavelet, windowed Fourier or wavelet-packet transform for the detection of events in noisy signals or for data compression. A major obstacle for their use is that a tailored efficient operator acting on the transform coefficients for altering the width of the wave packets does not exist. However, by virtue of a curious property of the Gabor functions it is possible to change the width of the wave packets using just one-dimensional convolutions with very short kernels. The cost of a wavelet-type transform based on the scheme presented below is similar to that of a low order wavelet transform for a compact kernel and significantly less than the algorithme à trous. The scheme can hence easily be employed for the processing of signals in real time. 相似文献
82.
The main goal of the present paper is to sharpen some results about the error made when the Wild sums, used to represent the solution of the Kac analog of Boltzmann’s equation, are truncated at the n-th stage. More precisely, in Carlen, Carvalho and Gabetta (J. Funct. Anal.
220: 362–387 (2005)), one finds a bound for the above-mentioned error which depends on (an
Λ+ε). On the one hand, it is shown that Λ, the least negative eigenvalue of the linearized collision operator, is the best possible exponent. On the other hand, ε is an extra strictly positive number and a a positive coefficient which depends on ε too. Thus, it is interesting to check whether ε can be removed from the above bound. According to the aforesaid reference, this problem is studied here by means of the probability distribution of the depth of a leaf in a McKean random tree. In fact, an accurate study of the probability generating function of such a depth leads to conclude that the above bound can be replaced with (a′ n
Λ). 相似文献
83.
Akinari Nakagawa 《Optical Review》2003,10(1):47-52
It has been noticed that observed spectral line profiles by the SOHO ultraviolet coronagraph spectrometer (SOHO/UVCS) are contaminated by a so-called detector effect, and an iterative correction of observed profiles by convolution with a zero-integral function has been employed to remove this unwanted effect on UVCS detectors. It is shown here that this iteration procedure using a zero-integral function can be replaced by an only-once application of convolution. For zero-integral functions of exp[- |x|/L]-type, the convolution function in this method is proved to have exactly the same, but narrower (steeper), functional form as the original one. These results are also valid, with some modifications, for the discrete case used in numerical calculation. 相似文献
84.
In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that Tω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show Tω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply Tω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability. 相似文献
85.
Marek Bożejko Anna Dorota Krystek Łukasz Jan Wojakowski 《Mathematische Zeitschrift》2006,253(1):177-196
In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution
is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined
with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive.
Partially sponsored with KBN grant no 2P03A00723 and RTN HPRN-CT-2002-00279. 相似文献
86.
B. G. Vakulov 《Mathematical Notes》2006,80(5-6):645-657
In this paper, we study the images of operators of the type of spherical potential of complex order and of spherical convolutions with kernels depending on the inner product and having a spherical harmonic multiplier with a given asymptotics at infinity. Using theorems on the action of these operators in Hölder-variable spaces, we construct isomorphisms of these spaces. In Hölder spaces of variable order, we study the action of spherical potentials with singularities at the poles of the sphere. Using stereographic projection, we obtain similar isomorphisms of Hö lder-variable spaces with respect to n-dimensional Euclidean space (in the case of its one-point compactification) with some power weights. 相似文献
87.
I. B. Simonenko 《Mathematical Notes》2005,78(1-2):239-250
We study the asymptotic behavior of the averaged f-trace of a truncated generalized multidimensional discrete convolution operator as the truncation domain expands. By definition, the averaged f-trace of a finite-dimensional operator A is equal to
, where n is the dimension of the space in which the operator A acts, the set of numbers γk, k = 1,..., n, is the complete collection of eigenvalues of the operator A, counting multiplicity; a generalized discrete convolution is an operator from the closure of the algebra generated by discrete convolution operators and by operators of multiplication by functions admitting a continuous continuation onto the sphere at infinity.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 265–277.Original Russian Text Copyright © 2005 by I. B. Simonenko. 相似文献
88.
We define a functional analytic transform involving the Chebyshev polynomials Tn(x), with an inversion formula in which the Möbius function μ(n) appears. If s∈C with Re(s)>1, then given a bounded function from [−1,1] into C, or from C into itself, the following inversion formula holds:
89.
In this paper, we define the quadratic-phase Fourier wavelet transform (QPFWT) and discuss its basic properties including convolution for QPFWT. Further, inversion formula and the Parseval relation of QPFWT are also discussed. Continuity of QPFWT on some function spaces are studied. Moreover, some applications of quadratic-phase Fourier transform (QPFT) to solve the boundary value problems of generalized partial differential equations. 相似文献
90.
ABSTRACTIn this paper, we introduce a discrete convolution involving both the Fourier sine and cosine series. We study Young's type inequality and a discrete transform related to this convolution and solve in closed form a class of discrete Toeplitz plus Hankel equations. 相似文献