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1.
Much of the recent literature on risk measures is concerned with essentially bounded risks in L
∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on L
p
spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded
random variables. The various continuity properties of risk measures can be interpreted as robustness properties and are useful
tools for approximations. As particular examples of risk measures on L
p
we discuss the expected shortfall and the shortfall risk. In the final part of the paper we consider the optimal risk allocation
problem for L
p
risks. 相似文献
2.
We prove a fixed point theorem for a family of Banach spaces including notably L 1 and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the “derivation problem” studied since the 1960s. 相似文献
3.
In this article we study the problem of extending Fourier
Multipliers on L
p
(T) to those on L
p
(R)
by taking convolution with a kernel, called a summability
kernel. We characterize the space of such kernels
for the cases p = 1 and p = 2. For other values of p we give a
necessary condition for a function to be a
summability kernel. For the case p = 1, we present
properties of measures which are transferred from M(T) to
M(R) by summability kernels. Furthermore it is
shown that every l
p
sequence can be extended to some
L
q
(R) multipliers for certain values of p and q. 相似文献
4.
Given
, a compact abelian group G and a function
, we identify the maximal (i.e. optimal) domain of the convolution
operator
(as an operator from Lp(G) to itself). This is the
largest Banach function space (with order continuous norm) into which Lp(G)
is embedded and to which
has a continuous extension, still with values
in Lp(G). Of course, the optimal domain depends on p and g. Whereas
is compact, this is not always so for the extension of
to its optimal domain.
Several characterizations of precisely when this is the case are presented. 相似文献
5.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-invariants of Riemannian foliations
Luis Sanguiao 《Annals of Global Analysis and Geometry》2008,33(3):271-292
For a Riemannian foliation on a closed manifold M, we define L
2-spectral sequence Betti numbers and spectral sequence Novikov–Shubin invariants. The spectral sequence of the lift of to the universal covering of M is used in the definitions. These invariants are natural extensions of the L
2-Betti numbers and the Novikov–Shubin invariants of differentiable manifolds. It is shown that these numbers are invariant
by foliated homotopy equivalences, and they are computed for several examples.
相似文献
6.
Marius A. S. Irgens 《Mathematische Zeitschrift》2004,247(3):611-617
Let be a bounded domain in Cn and let L2h() be the L2-holomorphic functions on . We show that the envelope of holomorphy and the L2h()-envelope of holomorphy of differ by at most a pluripolar set.Mathematics Subject Classification (2000): 32D10, 32A36, 32U30This article is based on work the author did during his Ph.D. studies at the University of Michigan under the supervision of John Erik Fornæss. 相似文献
7.
Functions whose translates span L
p
(R) are called L
p-cyclic functions. For a fixed
p \memb [1, \infty], we construct Schwartz-class functions which are L
r
-cyclic for r > p and not L
r
-
cyclic for r \le p. We then construct Schwartz-class functions which are L
r
-cyclic for r \ge p and
not L
r
-cyclic for r < p. The constructions differ for p \memb (1, 2) and p > 2. 相似文献
8.
In this paper the optimal L
2 error estimates of the finite volume element methods (FVEM) for Poisson equation are discussed on quadrilateral meshes. The
trial function space is taken as isoparametric bilinear finite element space on quadrilateral partition, and the test function
space is defined as piecewise constant space on dual partition. Under the assumption that all elements on quadrilateral meshes
are O(h
2) quasi-parallel quadrilateral elements, we prove convergence rate to be O(h
2) in L
2 norm. 相似文献
9.
For any complex valued L
p
-function b(x), 2 ≤ p < ∞, or L
∞-function with the norm ‖b↾L
∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d
2/dx
2 + x
2 + b(x) in L
2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L
2(ℝ). 相似文献
10.
Y-K Chen 《The Journal of the Operational Research Society》2007,58(3):337-345
Varying three parameters of the Hotelling's T2 control chart, namely, the sample size, the sampling interval length, and the action limit, results in a great improvement over the traditional T2 control chart particularly for the small process shift. This paper presents the economic model for designing the variable parameters T2 chart. In the economic design, a cost function is constructed, involving the cost of sampling and testing, the cost of false alarm, the cost to detect and remove the assignable cause, and the cost when the process is operating out-of-control. Also, a heuristic method of finding optimal values of adaptive design parameters for minimizing the cost function is presented. Variable and fixed parameters T2 control charts are compared with respect to the expected loss per unit time. Furthermore, the effects of the initial sample number (used for estimating the parameters of F-distribution) upon the operating cost and adaptive design parameters are examined. 相似文献
11.
Sun-Sig Byun 《Journal of Evolution Equations》2007,7(3):415-428
This work treats Lp regularity theory for weak solutions of parabolic equations in divergence form with discontinuous coefficients on nonsmooth
domains. We essentially obtain an optimal condition on the coefficients under which the global W1,p regularity theory holds.
This work was supported by SNU foundation in 2005. 相似文献
12.
Brian Clarke 《Annals of Global Analysis and Geometry》2011,39(2):131-163
We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate
the topology on the manifold of metrics induced by the distance function of the L
2 Riemannian metric—so-called because it induces an L
2 topology on each tangent space. It turns out that this topology on the tangent spaces gives rise to an L
1-type topology on the manifold of metrics itself. We study this new topology and its completion, which agrees homeomorphically
with the completion of the L
2 metric. We also give a user-friendly criterion for convergence (with respect to the L
2 metric) in the manifold of metrics. 相似文献
13.
We use microlocal and paradifferential techniques to obtain L
8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary.
The result leads to optimal L
q
bounds, in the range 2⩽q⩽∞, for L
2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds
with boundary. We also establish new sharp L
q
estimates in higher dimensions for a range of exponents q̅n⩽q⩽∞.
The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668. 相似文献
14.
Jesse Peterson 《Inventiones Mathematicae》2009,175(2):417-433
We introduce the notion of L
2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing
of 1-cohomology into the left regular representation of a group. We show that L
2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that if M is a free product
of diffuse von Neumann algebras, or if M=LΓ where Γ is a finitely generated group with β1
(2)(Γ)>0, then any nonamenable regular subfactor of M is prime and does not have properties Γ or (T). In particular this gives a new approach for showing solidity for a free group
factor thus recovering a well known recent result of N. Ozawa. 相似文献
15.
We study here L1-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for L1-convergence of double cosine trigonometric series.Also,the results obtained by Moricz[1],[2] are particular cases of ours. 相似文献
16.
Patrick LaVictoire 《Journal d'Analyse Mathématique》2011,113(1):241-263
We present a modified version of Buczolich and Mauldin’s proof that the sequence of square numbers is universally L
1-bad. We extend this result to a large class of sequences, including the dth powers and the set of primes. Furthermore, we show that any subsequence of the averages taken along these sequences is
also universally L
1-bad. 相似文献
17.
For q ≥ 0, Olsen [1] has attained the exact rate of convergence of the L
q
-spectrum of a self-similar measure and showed that the so-called empirical multifractal moment measures converges weakly
to the normalized multifractal measures. Unfortunately, nothing is known for q < 0. Indeed, the problem of analysing the L
q
- spectrum for q < 0 is generally considered significantly more difficult since the L
q
-spectrum is extremely sensitive to small variations of μ for q < 0. In [2] we showed that self-similar measures satisfying the Open Set Condition (OSC) are Ahlfors regular and, using this
fact, we obtained the exact rate of convergence of the L
q
-spectrum of a self-similar measure satisfying the OSC for q < 0. In this paper, we apply the results from [2] to show the empirical multifractal q’th moment measures of self-similar
measures satisfying the OSC converges weakly to the normalized multifractal Hausdorff measures for q < 0.
Authors’ addresses: Jiaqing Xiao, School of Science, Wuhan University of Technology, Wuhan 430070, China; Wu Min, School of
Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China 相似文献
18.
Heinrich P. Lotz 《Positivity》2008,12(1):119-132
We show that in the dual of Weak L1 the subspace of all rearrangement invariant continuous linear functionals is lattice isometric to a space L1(μ) and is the linear hull of the maximal elements of the dual unit ball. We also show that the dual of Weak L1 contains a norm closed weak* dense ideal which is lattice isometric to an ℓ1-sum of spaces of type C(K).
Helmut H. Schaefer in memoriam 相似文献
19.
We give a characterization of structurally stable diffeomorphisms by making use of the notion of L
p
-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C
1-interior of the set of diffeomorphisms having L
p
-shadowing property. 相似文献
20.
We show that for each positive integerk there is ak×k matrixB with ±1 entries such that puttingE to be the span of the rows of thek×2k matrix [√kI
k,B], thenE,E
⊥ is a Kashin splitting: TheL
1
2k
and theL
2
2k
are universally equivalent on bothE andE
⊥. Moreover, the probability that a random ±1 matrix satisfies the above is exponentially close to 1.
Supported by the Israel Science Foundation. 相似文献