| 1. |
- Carro, Maria J., et al.
(författare)
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Real interpolation for divisible cones
- 1999
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Ingår i: Proceedings of the Edinburgh Mathematical Society. - 0013-0915 .- 1464-3839. ; 42:2, s. 285-304
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Tidskriftsartikel (refereegranskat)abstract
- We give necessary and sufficient conditions on a general cone of positive functions to satisfy the Decomposition Property (DP) introduced in [5] and connect the results with the theory of interpolation of cones introduced by Sagher [9]. One of our main result states that if Q satisfies DP or equivalently is divisible, then for the quasi-normed spaces E0 and E1, According to this formula, it yields that the interpolation theory for divisible cones can be easily obtained from the classical theory
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| 2. |
- Carro, Maria J., et al.
(författare)
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S-divisibility property and a Holmstedt type formula
- 1999
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Ingår i: Journal of Approximation Theory. - : Elsevier BV. - 0021-9045 .- 1096-0430. ; 98:1, s. 1-24
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Tidskriftsartikel (refereegranskat)abstract
- Given a conePof positive functions and an operatorS: →Pwith an additive group, we extend the concept ofK-divisibility to get some new formulas for theK-functional of finite families of lattices. Applications are given in the setting of rearrangement invariant spaces and weighted Lorentz spaces. As a consequence of our results, we also obtain a generalized Holmstedt formula due to Asekritova
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| 3. |
- Ericsson, Stefan, et al.
(författare)
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An analysis method for sampling in shift-invariant spaces
- 2005
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Ingår i: International Journal of Wavelets, Multiresolution and Information Processing. - 0219-6913 .- 1793-690X. ; 3:3, s. 301-319
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Tidskriftsartikel (refereegranskat)abstract
- A subspace V of L2(ℝ) is called shift-invariant if it is the closed linear span of integer-shifted copies of a single function.As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method to derive both new results and relatively simple proofs of some previously known results. Among these are some results of rather general nature and some more specialized results for B-spline wavelets. The main problem under study is to find a shift x0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x0 + k + δk))k∈ℤ, either when all δk = 0 or in the irregular sampling case with an upper bound supk|δk| < δ.
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| 4. |
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| 5. |
- Ericsson, Stefan
(författare)
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Certain reiteration and equivalence results for the Cobos-Peetre polygon interpolation method
- 1999
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Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 85:2, s. 301-319
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Tidskriftsartikel (refereegranskat)abstract
- We prove some reiteration formulas for the Cobos-Peetre polygon method for $n+1$ tuples that consists of spaces $A_i$ where $A_i$ is of class $\theta_i$ with respect to a compatible pair $(X,Y)$. If $\theta_i$ is suitably chosen, the $J$- and $K$-method coincides and is equal to a space $(X,Y)_{\nu,q}$. For arbitrary chosen $\theta_i$ the $J$- and $K$-spaces will not, in general, coincide. In particular, we show that interpolation of Lorentz spaces over the unit square yields that the $K$-space is the sum of two Lorentz spaces whereas the $J$-space is the intersection of the same two Lorentz spaces.
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| 6. |
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| 7. |
- Ericsson, Stefan
(författare)
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Descriptions of some K functionals for three spaces and reiteration
- 1999
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 202:1, s. 29-41
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Tidskriftsartikel (refereegranskat)abstract
- We prove some equivalence formulas for the K functional for three spaces. In particular we calculate K(t, s, f, Lp0, Lp1, Lp2). We also give an integral formula connecting the K functional for triples of the type (A0, A1, A2), where A1 is of class C(θ, A0,A2), with the K functional for the pair (A0, A2). This formula is used to prove a reiteration formula for interpolation of the triple (A0, Al, A2) when Ai is of class C(θi, X, Y)
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| 8. |
- Ericsson, Stefan, et al.
(författare)
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Efficient wavelet prefilters with optimal time-shifts
- 2005
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Ingår i: IEEE Transactions on Signal Processing. - 1053-587X .- 1941-0476. ; 53:7, s. 2451-2461
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Tidskriftsartikel (refereegranskat)abstract
- A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain postfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.
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| 9. |
- Ericsson, Stefan
(författare)
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Exact descriptions of some K and E functionals
- 1997
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Ingår i: Journal of Approximation Theory. - : Elsevier BV. - 0021-9045 .- 1096-0430. ; 90:1, s. 75-87
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Tidskriftsartikel (refereegranskat)abstract
- Exact formulas for theKfunctional of some quasi-Banach couples of the type (X,L∞;) are obtained. In particular we can cover the cases whenX=Lp, q(Lorentzspaces), 0
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| 10. |
- Ericsson, Stefan
(författare)
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Generalized sampling in shift invariant spaces with frames
- 2012
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Ingår i: Acta Mathematica Sinica. English series. - : Springer Science and Business Media LLC. - 1439-8516 .- 1439-7617. ; 28:9, s. 1823-1844
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Tidskriftsartikel (refereegranskat)abstract
- Generalized sampling in a shift invariant subspace V of L 2(ℝ) is considered. A function f in V is processed with different filters L m and then one tries to reconstruct f from the samples L mf(j′k). We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question: How to obtain dual frames with compact support?
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