共查询到20条相似文献,搜索用时 15 毫秒
1.
L.G. Marcoci L.E. Persson I. Popa N. Popa 《Journal of Mathematical Analysis and Applications》2009,360(1):67-80
Let denote the space of all upper triangular matrices A such that limr→1−(1−r2)(A*C(r))′B(ℓ2)=0. We also denote by the closed Banach subspace of consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between and the Bergman–Schatten spaces . We also give a characterization of the more general Bergman–Schatten spaces , 1p<∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, Lp-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219–237] for classical Bergman spaces. 相似文献
2.
Approximation by polynomials in Bergman spaces of slice regular functions in the unit ball
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《Mathematical Methods in the Applied Sciences》2018,41(4):1619-1630
In this paper, we show that the set of quaternionic polynomials is dense in the Bergman spaces of slice regular functions in the unit ball, both of the first and of the second kind. Several proofs are presented, including constructive methods based on the Taylor expansion and on the convolution polynomials. In the last case, quantitative estimates in terms of higher‐order moduli of smoothness and of best approximation quantity are obtained. 相似文献
3.
We prove an identity for Hall–Littlewood symmetric functions labelled by the Lie algebra A2. Through specialization this yields a simple proof of the A2 Rogers–Ramanujan identities of Andrews, Schilling and the author. 相似文献
4.
The purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the Choi–Saigo–Srivastava operator for analytic functions and investigate various inclusion properties of these classes. Some interesting applications involving these and other classes of integral operators are also considered. 相似文献
5.
Semyon B. Yakubovich 《Journal of Approximation Theory》2004,131(2):175
We establish analogs of the Hausdorff–Young and Riesz–Kolmogorov inequalities and the norm estimates for the Kontorovich–Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in Lp spaces, 1p∞. Boundedness properties of the Kontorovich–Lebedev transform and its convolution operator are investigated. In certain cases the least values of the norm constants are evaluated. Finally, it is conjectured that the norm of the Kontorovich–Lebedev operator is equal to . It confirms, for instance, by the known Plancherel-type theorem for this transform when p=2. 相似文献
6.
The Rudin–Shapiro transform (RST) is a linear transform derived from the remarkable Rudin–Shapiro polynomials discovered in 1951. The transform has the notable property of forming a spread spectrum basis for , i.e. the basis vectors are sequences with a nearly flat power spectrum. It is also orthogonal and Hadamard, and it can be made symmetric. This presentation is partly a tutorial on the RST, partly some new results on the symmetric RST that makes the transform interesting from an applicational point-of-view. In particular, it is shown how to make a very simple O(NlogN) implementation, which is quite similar to the Haar wavelet packet transform. 相似文献
7.
Fabrizio Colombo Jonathan Gantner Tim Janssens 《Mathematical Methods in the Applied Sciences》2016,39(18):5582-5606
In this paper, we introduce the Schatten class and the Berezin transform of quaternionic operators. The first topic is of great importance in operator theory, but it is also necessary to study the second one, which requires the notion of trace class operators, a particular case of the Schatten class. Regarding the Berezin transform, we give the general definition and properties. Then we concentrate on the setting of weighted Bergman spaces of slice hyperholomorphic functions. Our results are based on the S‐spectrum of quaternionic operators, which is the notion of spectrum that appears in the quaternionic version of the spectral theorem and in the quaternionic S‐functional calculus. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
We prove analogs of the heat kernel transform inversion formulae of Golse, Leichtnam and the author [E. Leichtnam, F. Golse, M. Stenzel, Intrinsic microlocal analysis and inversion formulae for the heat equation on compact real-analytic Riemannian manifolds, Ann. Sci. École Norm. Sup. (4) 29 (6) (1996) 669–736. MR1422988 (97h:58153), Theorems 0.3, 0.4] in the setting of a Riemannian symmetric space of Helgason's non-compact type. 相似文献
9.
Pan Lian Gejun Bao Hendrik De Bie Denis Constales 《Mathematical Methods in the Applied Sciences》2017,40(10):3666-3675
In this paper, we introduce a new generalization of the Helgason–Fourier transform using the angular Dirac operator on both the hyperboloid and unit ball models. The explicit integral kernels of even dimension are derived. Furthermore, we establish the formal generating function of the even dimensional kernels. In the computations, fractional integration plays a key unifying role. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
M. C. Cmara A. F. dos Santos N. Manojlovi 《Mathematical Methods in the Applied Sciences》2001,24(13):993-1020
A generalization to N×N of the 2×2 Daniele–Khrapkov class of matrix‐valued functions is proposed. This class retains some of the features of the 2×2 Daniele–Khrapkov class, in particular, the presence of certain square‐root functions in its definition. Functions of this class appear in the study of finite‐dimensional integrable systems. The paper concentrates on giving the main properties of the class, using them to outline a method for the study of the Wiener–Hopf factorization of the symbols of this class. This is done through examples that are completely worked out. One of these examples corresponds to a particular case of the motion of a symmetric rigid body with a fixed point (Lagrange top). Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
11.
A. Passian H. Simpson S. Kouchekian S.B. Yakubovich 《Journal of Mathematical Analysis and Applications》2009,360(2):380-390
A proof of an orthogonality relation for the MacDonald's functions with identical arguments but unequal complex lower indices is presented. The orthogonality is derived first via a heuristic approach based on the Mehler–Fock integral transform of the MacDonald's functions, and then proved rigorously using a polynomial approximation procedure. 相似文献
12.
Fred Brackx Hennie De Schepper Nele De Schepper Frank Sommen 《Mathematical Methods in the Applied Sciences》2009,32(5):606-630
Clifford analysis is a higher‐dimensional function theory offering a refinement of classical harmonic analysis, which has proven to be an appropriate framework for developing higher‐dimensional continuous wavelet transforms, the construction of the wavelets being based on generalizations to a higher dimension of classical orthogonal polynomials on the real line. More recently, Hermitean Clifford analysis has emerged as a new branch of Clifford analysis, offering yet a refinement of the standard Euclidean case; it focusses on so‐called Hermitean monogenic functions, i.e. simultaneous null solutions of two Hermitean Dirac operators. In this Hermitean setting, Clifford–Hermite polynomials and their associated families of wavelet kernels have been constructed starting from a Rodrigues formula involving both Hermitean Dirac operators mentioned. Unfortunately, the property of the so‐called vanishing moments of the corresponding mother wavelets, ensuring that polynomial behaviour in the analyzed signal is filtered out, is only partially satisfied and has to be interpreted with care, the underlying mathematical reason being the fact that the Hermitean Clifford–Hermite polynomials show a too restrictive structure. In this paper, we will remediate this drawback by considering generalized Hermitean Clifford–Hermite polynomials, involving in their definition homogeneous Hermitean monogenic polynomials. The ultimate goal being the construction of new continuous wavelet transforms by means of these polynomials, we first deeply investigate their properties, amongst which are their connection with the traditional Laguerre polynomials, their structure and recurrence relations. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
13.
Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space of finite interval and the Paley–Wiener space of bandlimited functions on the real line. No other system of classical orthogonal functions is known to obey this unique property. This raises the question of whether they possess these properties in Clifford analysis. The aim of the article is to answer this question and extend the results to more flexible integral transforms, such as offset linear canonical transform. We also illustrate how to use the generalized Clifford PSWFs (for offset Clifford linear canonical transform) we derive to analyze the energy preservation problems. Clifford PSWFs is new in literature and has some consequences that are now under investigation. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
14.
Signal moments for the short‐time Fourier transform associated with Hardy–Sobolev derivatives
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M. Liu K.I. Kou J. Morais P. Dang 《Mathematical Methods in the Applied Sciences》2015,38(13):2719-2730
The short‐time Fourier transform has been shown to be a powerful tool for non‐stationary signals and time‐varying systems. This paper investigates the signal moments in the Hardy–Sobolev space that do not usually have classical derivatives. That is, signal moments become valid for non‐smooth signals if we replace the classical derivatives by the Hardy–Sobolev derivatives. Our work is based on the extension of Cohen's contributions to the local and global behaviors of the signal. The relationship of the moments and spreads of the signal in the time, frequency and short‐time Fourier domain are established in the Hardy–Sobolev space. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
15.
Amedeo Altavilla 《复变函数与椭圆型方程》2015,60(1):59-77
The theory of slice regular functions over the quaternions, introduced by Gentili and Struppa in 2007, was born on balls centred in the origin and has been extended to more general domains that intersect the real axis in a work of 2009 in collaboration with Colombo and Sabadini. This hypothesis can be overcome using the theory of stem functions introduced by Ghiloni and Perotti in 2011, in the context of real alternative algebras. In this paper, I will recall the notion and the main properties of stem functions. After that I will introduce the class of slice regular functions induced by stem functions and, in this set, I will extend the identity principle, the maximum and minimum modulus principles and the open mapping theorem. Differences will be shown between the case when the domain does or does not intersect the real axis. 相似文献
16.
mdat can 《Numerical Methods for Partial Differential Equations》2021,37(1):118-130
In this paper, first, we prove the weighted Hermite–Hadamard–Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right‐sides of weighted Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in absolute value at certain powers are convex. The results presented here would provide extensions of those given in earlier works. 相似文献
17.
A proof of the fact that the Hilbert transform can be extended as an isometry to L2 is obtained by real variable methods using the Hermite functions. 相似文献
18.
The structured higher-order Bessel-type linear ordinary differential equations were first discovered in 1994. There is a denumerable infinity of these higher-order equations, all of then of even-order.These differential equations possess many of the properties of the classical second-order Bessel differential equation, but these higher-order cases bring remarkable new analytic structures. In many ways it is sufficient to study the properties of the fourth-order Bessel-type differential equation to be able to assess the corresponding properties of the sixth-and higher-order cases.This paper follows a number of earlier papers devoted to the study of the fourth-order case. These publications show the connections between the special function properties of solutions of the differential equation, and the properties of linear differential operators generated by the associated linear differential expression in certain weighted Lebesgue, and Lebesgue–Stieltjes function spaces.To follow the earlier papers on the study of the fourth-order Bessel-type differential equation, this present paper determines the form of the Fourier–Bessel-type series which best extends the classical theory of the second-order Fourier–Bessel series.In fact the Fourier–Bessel-type series are based on a new orthogonal system in terms of the regular eigensolutions of the fourth-order Bessel-type equation. The corresponding eigenvalues are obtained by restricting the spectral parameter to the zeros of an analytic function arising already in the Dini boundary conditions. 相似文献
19.
The goal of the paper is to prove generalizations of the classical Plancherel–Polya inequalities in which point-wise sampling of functions (δ-distributions) is replaced by more general compactly supported distributions on . As an application it is shown that a function , 1p∞, which is an entire function of exponential type is uniquely determined by a set of numbers {Ψj(f)}, , where {Ψj}, , is a countable sequence of compactly supported distributions. In the case p=2 a reconstruction method of a Paley–Wiener function f from a sequence of samples {Ψj(f)}, , is given. This method is a generalization of the classical result of Duffin–Schaeffer about exponential frames on intervals. 相似文献
20.
《Mathematische Nachrichten》2018,291(14-15):2236-2251
We describe exactly and fully which of the spaces of holomorphic functions in the title are included in which others. We provide either new results or new proofs. More importantly, we construct explicit functions in each space that show our relations are strict and the best possible. Many of our inclusions turn out to be sharper than the Sobolev imbeddings. 相似文献