An Lp-Lq-Version of Morgan’s Theorem for the Dunkl-Bessel Transform

In this paper, we give an L^p-L^q-version of Morgans theorem for the Dunkl-Bessel transform on More precisely, we prove that for all and then for all measurable function f on the conditions and imply f = 0, if and only if where are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004     

Stability of the Cauchy congruence on restricted domain

Let S be a real interval with , and be a function satisfying We show that if h is Lebesgue or Baire measurable, then there exists such that That result is motivated by a question of E. Manstaviius. Received: 11 February 2003     

Maximum decay rate for the nonlinear Schrödinger equation

In this paper, we consider global solutions for the following nonlinear Schrödinger equation in with and We show that no nontrivial solution can decay faster than the solutions of the free Schrödinger equation, provided that u(0) lies in the weighted Sobolev space in the energy space, namely or in according to the different cases.     

Evolution systems and perturbations of generators of strongly continuous groups

Suppose A generates a strongly continuous linear group on a Banach space X and B is a linear operator on X. It is shown that an extension of generates a strongly continuous semigroup if and only if the family of operators has an appropriate evolution system. This produces simple sufficient conditions for an extension of to generate a strongly continuous semigroup, including

A Constructive Proof of the Generalized Gelfand Isomorphism

Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius -homomorphism. For , this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space, the th symmetric power of X, and the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map defined by the formula identifies the space with the space of all Frobenius -homomorphisms of the algebra into with the weak topology.     

On automorphisms of the symmetrized bidisc

We characterize the group Aut for the symmetrized bidisc

Subdominant Matroid Ultrametrics

Given a matroid M on the ground set E, the Bergman fan or space of M-ultrametrics, is a polyhedral complex in which arises in several different areas, such as tropical algebraic geometry, dynamical systems, and phylogenetics. Motivated by the phylogenetic situation, we study the following problem: Given a point in we wish to find an M-ultrametric which is closest to it in the -metric. The solution to this problem follows easily from the existence of the subdominant M-ultrametric: a componentwise maximum M-ultrametric which is componentwise smaller than . A procedure for computing it is given, which brings together the points of view of matroid theory and tropical geometry. When the matroid in question is the graphical matroid of the complete graph K_n, the Bergman fan parameterizes the equidistant phylogenetic trees with n leaves. In this case, our results provide a conceptual explanation for Chepoi and Fichets method for computing the tree that most closely matches measured data.Received August 12, 2004     

Brownian Martingales and Some New Results on Interpolation of Hardy Spaces

Let H₁( ) be the usual Hardy space on . We show that the couple (H₁( ), L( ) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH₁( ) +L( ) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H₁( ) to L₁( ) and also from L( ) to L( ); (ii) V(Nf)=f, V is similtaneously bounded from L₁( ) to H₁( ) and from L( ) to L( ) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (L_p( ), BMO ( )) for every 1相似文献   

Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero

Under the cancellation property and a certain Dini-type condition on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous functions of degree zero, are bounded from to , from to , and from to for .     

Stochastic Partial Differential Equations on Manifolds~II. Nonlinear Filtering

The conditional law of an unobservable component x(t) of a diffusion (x(t),y(t)) given the observations {y(s):s[0,t]} is investigated when x(t) lives on a submanifold of . The existence of the conditional density with respect to a given measure on is shown under fairly general conditions, and the analytical properties of this density are characterized in terms of the Sobolev spaces used in the first part of this series.     

Increasing functions and inverse Santaló inequality for unconditional functions

Let be a convex function and be its Legendre tranform. It is proved that if is invariant by changes of signs, then . This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond. The proof involves a general result on increasing functions on together with a functional form of Lozanovskii’s lemma. In the last section, we prove that for some c > 0, one has always . This generalizes a result of B. Klartag and V. Milman.      

Decay rates of solutions to dissipative nonlinear evolution equations with ellipticity

In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects

Discussing Knarr's 2-Surface of \mathbb{R} 4 which Generates the First Single Shift Plane

The generating line of the first single shift plane (cf. [11, p. 435]) is a 2-surface of ⁴ which we call the the affine part of Knarr's surface. We compute all affinities leaving invariant. After embedding ⁴ into PG(4, ) we calculate the uniquely determined projective closure _Kn of . Using a suitable projection we transform questions on Knarr's surface to questions on Cayley's surface in PG(3, ). In this way we determine all planes carrying 1-dimensional algebraic varieties of _Kn . We exhibit all automorphic collineations of _Kn .     

Lattices of interpretability types of varieties

Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root _p(x) for every p , is a variety of -modules over a normal field , contained in , and G_n is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ub_f are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.