共查询到20条相似文献,搜索用时 11 毫秒
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2.
Mohammad Masjed-Jamei 《Journal of Computational and Applied Mathematics》2010,234(2):365-374
Let T,U be two linear operators mapped onto the function f such that U(T(f))=f, but T(U(f))≠f. In this paper, we first obtain the expansion of functions T(U(f)) and U(T(f)) in a general case. Then, we introduce four special examples of the derived expansions. First example is a combination of the Fourier trigonometric expansion with the Taylor expansion and the second example is a mixed combination of orthogonal polynomial expansions with respect to the defined linear operators T and U. In the third example, we apply the basic expansion U(T(f))=f(x) to explicitly compute some inverse integral transforms, particularly the inverse Laplace transform. And in the last example, a mixed combination of Taylor expansions is presented. A separate section is also allocated to discuss the convergence of the basic expansions T(U(f)) and U(T(f)). 相似文献
3.
Deguang Han 《Transactions of the American Mathematical Society》2008,360(6):3307-3326
Let be a frame for a Hilbert space . We investigate the conditions under which there exists a dual frame for which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is obtained in terms of the frame excess. For a frame induced by a projective unitary representation of a group , it is possible that can have a Parseval dual, but does not have a Parseval dual of the same type. The primary aim of this paper is to present a complete characterization for all the projective unitary representations such that every frame (with a necessary lower frame bound condition) has a Parseval dual of the same type. As an application of this characterization together with a result about lattice tiling, we prove that every Gabor frame (again with the same necessary lower frame bound condition) has a Parseval dual of the same type if and only if the volume of the fundamental domain of is less than or equal to .
4.
Ole Christensen 《Journal of Fourier Analysis and Applications》2000,6(1):79-91
A frame in a Hilbert space
allows every element in
to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculations of
those coefficients and many other situations where frames occur, requires knowledge of the inverse frame operator. But usually
it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce
a method for approximation of the inverse frame operator using finite subsets of the frame. In particular this allows to approximate
the frame coefficients (even inl
2) using finite-dimensional linear algebra. We show that the general method simplifies in the important cases of Weil-Heisenberg
frames and wavelet frames. 相似文献
5.
A unified abstract framework for the multilevel decomposition of both Banach and quasi-Banach spaces is presented. The characterization
of intermediate spaces and their duals is derived from general Bernstein and Jackson inequalities. Applications to compactly
supported biorthogonal wavelet decompositions of families of Besov spaces are also given.
The first author was partially supported by grants from MURST (40% Analisi Numerica) and ASI (Contract ASI-92-RS-89), whereas
the second author was partially supported by grants from MURST (40% Analisi Funzionale) and CNR (Progetto Strategico “Applicazioni
della Matematica per la Tecnologia e la Società”). 相似文献
6.
Deguang Han 《Journal of Functional Analysis》2009,256(1):129-1472
Let K and L be two full-rank lattices in Rd. We give a complete characterization for all the Gabor frames that admit tight dual of the same type. The characterization is given in terms of the center-valued trace of the von Neumann algebra generated by the left regular projective unitary representations associated with the time-frequency lattice K×L. Two applications of this characterization were obtained: (i) We are able to prove that every Gabor frame has a tight dual if and only if the volume of K×L is less than or equal to . (ii) We are able to obtain sufficient or necessary conditions for the existence of tight Gabor pseudo-duals for subspace Gabor frames in various cases. In particular, we prove that every subspace Gabor frame has a tight Gabor pseudo-dual if either the volume or v(K×L)?2. Moreover, if K=αZd, L=βZd with αβ=1, then a subspace Gabor frame G(g,L,K) has a tight Gabor pseudo-dual only when G(g,L,K) itself is already tight. 相似文献
7.
A. J. E. M. Janssen 《Journal of Fourier Analysis and Applications》1997,3(5):583-596
In this article we consider the question when one can generate a Weyl- Heisenberg frame for l
2
(ℤ) with shift parameters N, M
−1
(integer N, M) by sampling a Weyl-Heisenberg frame for L
2
(ℝ) with the same shift parameters at the integers. It is shown that this is possible when the window g ε L
2
(ℝ) generating the Weyl-Heisenberg frame satisfies an appropriate regularity condition at the integers. When, in addition,
the Tolimieri-Orr condition A is satisfied, the minimum energy dual window
o
γ ε L
2
(ℝ) can be sampled as well, and the two sampled windows continue to be related by duality and minimality. The results of this
article also provide a rigorous basis for the engineering practice of computing dual functions by writing the Wexler-Raz biorthogonality
condition in the time-domain as a collection of decoupled linear systems involving samples of g and
o
γ as knowns and unknowns, respectively. We briefly indicate when and how one can generate a Weyl-Heisenberg frame for the
space
of K-periodic sequences, where K=LCM (N, M), by periodization of a Weyl-Heisenberg frame for ℓ
2
ℤ with shift parameters N, M
−1
. 相似文献
8.
In [C.K. Chui and X.L. Shi, Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal., 24 (1993), 263–277], the authors proved that if
is a Gabor frame for
with frame bounds A and B, then the following two inequalities hold:
and
. In this paper, we show that similar inequalities hold for multi-generated irregular Gabor frames of the form
, where Δ
k
and Λ
k
are arbitrary sequences of points in
and
, 1 ≤ k ≤ r.
Corresponding author for second author
Authors’ address: Lili Zang and Wenchang Sun, Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China 相似文献
9.
Daniela Roşca 《Results in Mathematics》2006,49(1-2):171-184
We construct orthonormal bases of linear splines on a finite interval [a, b] and then we study the Fourier series associated to these orthonormal bases. For continuous functions defined on [a, b], we prove that the associated Fourier series converges pointwisely on (a, b) and also uniformly on [a, b], if it convergences pointwisely at a and b. 相似文献
10.
Richard Vale 《Linear algebra and its applications》2010,433(1):248-94
We define the symmetry group of a finite frame as a group of permutations on its index set. This group is closely related to the symmetry group of Vale and Waldron (2005) [12] for tight frames: they are isomorphic when the frame is tight and has distinct vectors. The symmetry group is the same for all similar frames, in particular for a frame, its dual and canonical tight frames. It can easily be calculated from the Gramian matrix of the canonical tight frame. Further, a frame and its complementary frame have the same symmetry group. We exploit this last property to construct and classify some classes of highly symmetric tight frames. 相似文献
11.
In this paper, we are concerned with biorthogonal Wilson bases having B-splines as well as powers of sinc functions as window
functions. We prove properties of B-splines and exponential Euler splines and use these properties to estimate the Riesz bounds
of the Wilson bases. 相似文献
12.
This article obtains the nonseparable version of wavelet packets onℝ
d and generalizes the “unstability” result of nonorthogonal wavelet packets in Cohen-Daubechies to higher dimensional cases.
Professor Ruilin Long died on August 13, 1996. 相似文献
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In this paper, we study the feasibility and stability of recovering signals in finite-dimensional spaces from unordered partial frame coefficients. We prove that with an almost self-located robust frame, any signal except from a Lebesgue measure zero subset can be recovered from its unordered partial frame coefficients. However, the recovery is not necessarily stable with almost self-located robust frames. We propose a new class of frames, namely self-located robust frames, that ensures stable recovery for any input signal with unordered partial frame coefficients. In particular, the recovery is exact whenever the received unordered partial frame coefficients are noise-free. We also present some characterizations and constructions for (almost) self-located robust frames. Based on these characterizations and construction algorithms, we prove that any randomly generated frame is almost surely self-located robust. Moreover, frames generated with cube roots of different prime numbers are also self-located robust. 相似文献
16.
WuZhengchang 《高校应用数学学报(英文版)》2001,16(2):171-177
Abstract. In this paper it is proved that Lp solutions of a refinement equation exist if and only ifthe corresponding subdivision scheme with suitable initial function converges in Lp without anyassumption on the stability of the solutions of the refinement equation. A characterization forconvergence of subdivision scheme is also given in terms of the refinement mask. Thus a com-plete answer to the relation between the existence of Lp solutions of the refinement equation andthe convergence of the corresponding subdivision schemes is given. 相似文献
17.
In this paper we prove two consequences of the subnormal character of the Hessenberg matrix D when the hermitian matrix M of an inner product is a moment matrix. If this inner product is defined by a measure supported on an algebraic curve in the complex plane, then D satisfies the equation of the curve in a noncommutative sense. We also prove an extension of the Krein theorem for discrete measures on the complex plane based on properties of subnormal operators. 相似文献
18.
In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems: for any ε∈(0, 1), there exists a measurable set E [0, 1)of measure bigger than 1-ε such that for any function f ∈ L~1[0, 1), it is possible to find a function g ∈ L~1[0, 1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing. 相似文献
19.
Marek Kossowski 《Annals of Global Analysis and Geometry》1993,11(3):237-251
A generic compact surfaceQ in Minkowski 3-Space is naturally stratified by the loci where the orthogonal line bundle is tangent to the next lower stratum,SP D
0 Q M3. To each component inD
0 we associate a light-like hypersurface and in turn a Lagrangian loop in the cotangent bundle of the circle. We then establish an inequality relating the Euler characteristic of the indefinite component ofQ with the total Gauß-Maslov index of the associated Lagrangian loops. 相似文献
20.
Mark Skandera 《Journal of Pure and Applied Algebra》2008,212(5):1086-1104
Using Du’s characterization of the dual canonical basis of the coordinate ring O(GL(n,C)), we express all elements of this basis in terms of immanants. We then give a new factorization of permutations w avoiding the patterns 3412 and 4231, which in turn yields a factorization of the corresponding Kazhdan-Lusztig basis elements of the Hecke algebra Hn(q). Using the immanant and factorization results, we show that for every totally nonnegative immanant and its expansion with respect to the basis of Kazhdan-Lusztig immanants, the coefficient dw must be nonnegative when w avoids the patterns 3412 and 4231. 相似文献