共查询到20条相似文献,搜索用时 11 毫秒
1.
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
2.
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
3.
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
4.
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
5.
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
6.
V. M. Kaplitskiĭ 《Siberian Mathematical Journal》2010,51(2):255-266
We show that Peetre’s classical interpolation theorem in weighted L
p
-spaces is carried over to some classes of nonlinear operators containing in particular the Lipschitz operators and operators
close to them in the properties satisfying less restrictive conditions than Lipschitz in each of the spaces of a Banach pair. 相似文献
7.
Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q ? E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from Lp to Lq is found. There exists a strictly singular but not superstrictly singular operator on Lp, provided that p ≠ 2. 相似文献
8.
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
9.
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
10.
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
11.
The paper extends the two notions of the dual mixed volumes and L
p
-intersection body to q-dual mixed volumes and L
p
-mixed intersection body, respectively. Inequalities for the star dual of L
p
-mixed intersection bodies are established. 相似文献
12.
13.
We obtain Lp-versions of theorems proved by J. L. Fernández and J. M. Rodríguez in the paper “The Exponent of Convergence of Riemann Surfaces, Bass Riemann Surfaces”, Ann. Acad. Sci. Fenn. Ser.A. I.Mathematica 15, 165–182 (1990). An important role in the proof of our results is due to the approach of V. M. Miklyukov and M. K. Vuorinen. In particular, we use the isoperimetric profile of hyperbolic domains. 相似文献
14.
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
15.
I. E. Simonov 《Proceedings of the Steklov Institute of Mathematics》2012,278(1):161-168
A recent modification of a classic Landau-Lifshitz equation that includes the socalled spin-transfer torque is widely recognized in physics community as a model of magnetization dynamics in certain nanodevices. Motivated by some experimental evidence, we introduce a generalization of this model, coupled Landau-Lifshitz equations with spin-transfer torque terms, and analyze it from dynamical systems standpoint. An explicit stability criterion for the critical points in terms of all parameters of the system is derived and illustrated with stability diagrams. Our analysis provides certain guidelines for the design of magnetic nanodevices with optimized response to control parameters. 相似文献
16.
G. Amirkhanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(3):127-134
Convergence of the greedy algorithm in Walsh system in L p , p > 1 is studied. It is proved that there exists a function in L p , 1 < p < 2, with greedy algorithm not converging in measure to that function. A continuous function with divergent in L p , p > 2, greedy algorithm is constructed and sufficient conditions for convergence of the greedy algorithm in L p , p > 1 are given. 相似文献
17.
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
18.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
where φ
r
is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3.
As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L
∞
r
, namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008. 相似文献
19.
We study the L
p
-saturation for the linear combination of Bernstein-Kantorovich operators. As a result we obtain the saturation class by using
K-functional as well as some modulus of smoothness.
Research supported by National Natural Science Foundation of China (10671019) and Zhejiang Provincial Natural Science Foundation
of China (102005). 相似文献
20.
Josef Dick Aicke Hinrichs Lev Markhasin Friedrich Pillichshammer 《Israel Journal of Mathematics》2017,218(1):489-510
In this paper we state a one-to-one connection between the maximal ratio of the circumradius and the diameter of a body (the Jung constant) in an arbitrary Minkowski space and the maximal Minkowski asymmetry of the complete bodies within that space. This allows to generalize and unify recent results on complete bodies and to derive a necessary condition on the unit ball of the space, assuming a given body to be complete. Finally, we state several corollaries, e.g. concerning the Helly dimension or the Banach–Mazur distance. 相似文献