共查询到20条相似文献,搜索用时 546 毫秒
1.
We discuss the L
p
(0 ≤ p < 1) minimization problem arising from sparse solution construction and compressed sensing. For any fixed 0 < p < 1, we prove that finding the global minimal value of the problem is strongly NP-Hard, but computing a local minimizer of
the problem can be done in polynomial time. We also develop an interior-point potential reduction algorithm with a provable
complexity bound and demonstrate preliminary computational results of effectiveness of the algorithm. 相似文献
2.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
3.
Morten Nielsen 《Journal of Geometric Analysis》2012,22(1):12-22
We consider a periodic matrix weight W defined on ℝ
d
and taking values in the N×N positive-definite matrices. For such weights, we prove transference results between multiplier operators on L
p
(ℝ
d
;W) and
Lp(\mathbb Td;W)L_{p}(\mathbb {T}^{d};W), 1<p<∞, respectively. As a specific application, we study transference results for homogeneous multipliers of degree zero. 相似文献
4.
Yu. S. Kolomoitsev 《Journal of Mathematical Sciences》2010,165(4):463-472
Let B be a set of integers with certain arithmetic properties. We obtain estimates of the best approximation of functions in the
space L
p
, 0 < p <1, by trigonometric polynomials that are constructed by the system
{eikx}k ? \mathbbZ\B \{e^{ikx}\}_{k\in \mathbb{Z}\backslash B} . Bibliography: 13 titles. 相似文献
5.
W.-D. Richter 《Lithuanian Mathematical Journal》2009,49(1):93-108
For p > 0, the l
n,p
-generalized surface measure on the l
n,p
-unit sphere is studied and used for deriving a geometric measure representation for l
n,p
-symmetric distributions having a density. 相似文献
6.
We obtain an isoperimetric inequality which estimate the affine invariant p-surface area measure on convex bodies. We also establish the reverse version of L
p
-Petty projection inequality and an affine isoperimetric inequality of Γ − p
K. 相似文献
7.
We show that if (p0, p1, ...) is the pn-sequence of a nontrivial algebra with one fundamental operation, then p1 ≥ p0. Moreover, if
, then p1 > 2p0.
Received April 21, 2003; accepted in final form November 28, 2005. 相似文献
8.
We study the solvabitlity of the Dirichlet problem for the heat operator in weighted Sobolev L
p
-spaces in noncylindrical paraboloid type domains with isolated characteristic points at the boundary. For any p > 1 we find a necessary and sufficient L
p
-solvability condition and establish an L
p
-estimate. The results are formulated in terms of Muckenhoupt type conditions on the weight. Bibliography: 10 titles. 相似文献
9.
We investigate the best approximations of sine-shaped functions by constants in the spaces Lp for p < 1. In particular, we find the best approximation of perfect Euler splines by constants in the spaces Lp for certain p(0,1).Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 745–762, June, 2004. 相似文献
10.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp(0〈p〈1)Spaces 总被引:1,自引:0,他引:1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
11.
Michael J. Johnson 《Constructive Approximation》2004,20(2):303-324
We show that the Lp-approximation order of surface spline interpolation
equals m+1/p for p in the range 1 \leq p \leq 2, where m is an integer
parameter which specifies the surface spline. Previously it was known that this
order was bounded below by m + &frac; and above by m+1/p. With
h denoting the fill-distance between the interpolation points and the domain
, we show specifically that the Lp()-norm of the error between f
and its surface spline interpolant is O(hm + 1/p) provided that f belongs
to an appropriate Sobolev or Besov space and that \subset
Rd is open, bounded, and has the C2m-regularity
property. We also show that the boundary effects (which cause the rate of
convergence to be significantly worse than O(h2m)) are confined to a
boundary layer whose width is no larger than a constant multiple of
h |log h|. Finally, we state numerical evidence which supports the
conjecture that the
Lp-approximation order of surface spline interpolation is m + 1/p for
2 < p \leq \infty. 相似文献
12.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献
13.
S. B. Yakubovich 《Lithuanian Mathematical Journal》2005,45(1):102-122
We establish the boundedness properties in L
p
for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in L
p
(R
+), 1 p 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 127–147, January–March, 2005. 相似文献
14.
V. E. Maiorov 《Ukrainian Mathematical Journal》2010,62(3):452-466
We study the approximation of the classes of functions by the manifold R
n
formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W
r
p
from the set R
n
of ridge functions in the space L
q
(B
d
) satisfies the sharp order n
-r/(d-1). 相似文献
15.
We show that for every odd integer p 1 there is an absolute positive
constantcp, so that the maximum cardinality of a set of vectors in Rn
such that the lp distance between
any pair is precisely 1, is at most cp
n log n.
We prove some upper bounds for other lp norms as well. 相似文献
16.
In this paper we study the L
p
-discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which
is also known as Roth net) with N points has L
p
-discrepancy (p an integer) of order (log N)/N, we show that there always exists a shift such that the digitally shifted Hammersley point set has L
p
-discrepancy (p an even integer) of order
which is best possible by a result of W. Schmidt. Further we concentrate on the case p = 2. We give very tight lower and upper bounds for the L
2-discrepancy of digitally shifted Hammersley point sets which show that the value of the L
2-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position
of these.
This work is supported by the Austrian Research Fund (FWF), Project P17022-N12 and Project S8305. 相似文献
17.
We determine the L
p
discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the L
p
discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound
on L
p
discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the
Hammersley point set and show that there always exist permutations such that the L
p
discrepancy of the generalized Hammersley point set is of best possible order. For the L
2 discrepancy such permutations are given explicitly.
F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research
Network “Analytic Combinatorics and Probabilistic Number Theory”. 相似文献
18.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
19.
We calculate the ordinal L p index defined in [3] for Rosenthal’s space X p , \({\ell_p}\) and \({\ell_2}\). We show that an infinite-dimensional subspace of L p \({(2 < p < \infty)}\) non-isomorphic to \({\ell_2}\) embeds in \({\ell_p}\) if and only if its ordinal index is the minimal possible. We also give a sufficient condition for a \({\mathcal{L}_p}\) subspace of \({\ell_p \oplus \ell_2}\) to be isomorphic to X p . 相似文献
20.
A. G. Bytsko 《Journal of Mathematical Sciences》2010,168(6):805-810
We consider the spectral resolution of a Uq (sl
2)-invariant solution R of the constant Yang–Baxter equation in the braid group form. It is shown that if the two highest coefficients in this resolution
are not equal, then R is either the Drinfeld R-matrix or its inverse. Bibliography: 13 titles. 相似文献