Abstract: We consider the C*-algebras constructed from certain hyperbolic dynamical systems. The construction, due to Ruelle, generalizes the C*-algebras of Cuntz and Krieger. We discuss relations between the C*-algebras, show the existence of natural asymptotically abelian systems and investigate the K-theory and E-theory of these C*-algebras.

Abstract: This article contains examples and applications of the notion of exact sequences of Hopf algebras.

Abstract: characterization of the spaces dual to weighted Lorentz spaces are given by means of reverse Holder inequalities (Theorems 2.1, 2.2). This principle of duality is then applied to characterize weight functions for which the identity operator, the Hardy-Littlewood maximal operator and the Hilbert transform are bounded on weighted Lorentz spaces.

Abstract: We estimate the density of resonances close to a critical curve, for strictly convex obstacles with analytic boundary. Contrary to the C ∞-case, already treated with Zworski, the estimates are in terms of dynamical quantities. A new feature in the proof is a certain averaging procedure.

Abstract: We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegýo and leads naturally to the Al-Salam-Chihara polynomials then to the Askey-Wilson polynomials, the big q-Jacobi polynomials and the biorthogonal rational functions of Al-Salam and Verma, and some recent biorthogonal functions of Al-Salam and Ismail.

Abstract: We completely determine the residual spectrum of the split exceptional group of type G 2, thus completing the work of Langlands and Moeglin-Waldspurger on the part of the residual spectrum attached to the trivial character of the maximal torus. We also give the Arthur parameters for the residual spectrum coming from Borel subgroups. The interpretation in terms of Arthur parameters explains the “bizarre” multiplicity condition in Moeglin-Waldspurger's work. It is related to the fact that the component group of the Arthur parameter is non-abelian.

Abstract: This paper is devoted to extending formulas for the geometric approximate subdifferential and the Clarke subdifferential of extended-real-valued functions on Banach spaces. The results are strong enough to include completely the finite dimensional setting.

Abstract: Some oscillation criteria are given for the second order neutral delay differential equation where τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

Abstract: Let X be a Banach space and . Let Π and Π0 be two subspaces of , the Banach space of bounded continuous functions from 𝕁 to X. We seek conditions under which Π + Π0 is closed in . This led to introduce a general space, which contains many classes of almost periodic type functions as subspaces. We prove some recent results on indefinite integral for the elements of these classes. We apply certain results on harmonic analysis to investigate solutions of differential equations. As an application we study specific spaces: the spaces of asymptotic and pseudo almost automorphic functions and their solutions of some ordinary quasi-linear and a non-linear parabolic partial differential equations.

Abstract: We complete our investigations of mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn (W 2, x) for Erdős weights W 2 = e -2Q . The archetypal example is Wk,α = exp(—Qk,α ), where α > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 ℝ satisfying it is necessary and sufficient that α > 1/p. This is, essentially, an extension of the Erdos-Turan theorem on L 2 convergence. In an earlier paper, we analyzed convergence for all p > 1, showing the necessity and sufficiency of using the weighting factor 1 + Q for all p > 4. Our proofs of convergence are based on converse quadrature sum estimates, that are established using methods of H. Konig.

Abstract: Let X be a d-dimensional continuous super-Brownian motion with branching rate epsilon, which might be described symbolically by the ''stochastic equation'' dX(t) = Delta*X(t)dt + root 2 epsilon X(t ...

Abstract: Generalized Riesz products similar to the type which arise as the spectral measure for a rank-one transformation are studied. A condition for the mutual singularity of two such measures is given. As an application, a probability space of transformations is presented in which almost all transformations are singular with respect to Lebesgue measure. AMS Subject Classification: Primary 28D03; Secondary 42A55, 47A35 0

Abstract: Let G(z) := (z-A0) Eg!i (1 ~ T~n)(* r^ ) where {A„ }„GZ is a sequence of real numbers such that |A„ — n\\ < A for some A > 0 and all « e Z . Extending an obvious property of sin irz to which the function G reduces when A = 0 we show that G\"A y is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.

Abstract: Existence of solutions to the nonlinear boundary value problem on the semi-infinite interval bounded on [0, ∞), are established. In the process we obtain new existence results for boundary value problems on compact intervals.

Abstract: Let k ≥ 2 be an integer. Let Ek (N) be the number of natural numbers not exceeding N which are not the sum of a prime and a k-th power of a natural number. Assuming the Riemann Hypothesis for all Dirichlet L-functions it is shown that Ek (N) ≪ N1-1/25k.

Abstract: Let G be a finite π-separable group, where π is a set of primes. The π-partial characters of G are the restrictions of the ordinary characters to the set of π-elements of G. Such an object is said to be irreducible if it is not the sum of two nonzero partial characters and the set of irreducible π- partial characters of G is denoted Iπ(G). (If p is a prime and π = p′, then Iπ(G) is exactly the set of irreducible Brauer characters at p.) From their definition, it is obvious that each partial character φ ∊ Iπ(G) can be “lifted” to an ordinary character χ ∊ Irr(G). (This means that φ is the restriction of χ to the π-elements of G.) In fact, there is a known set of canonical lifts Bπ(G) ⊆ Irr(G) for the irreducible π-partial characters. In this paper, it is proved that if 2 ∉ π, then there is an alternative set of canonical lifts (denoted Dπ(G)) that behaves better with respect to character induction. An application of this theory to M-groups is presented. If G is an M-group and S ⊆ G is a subnormal subgroup, consider a primitive character θ ⊆ Irr(S). It was known previously that if |G : S| is odd, then θ must be linear. It is proved here without restriction on the index of S that θ(1) is a power of 2.

Abstract: Let X be a Banach space and (f n ) n be a bounded sequence in L 1(X). We prove a complemented version of the celebrated Talagrand's dichotomy, i.e., we show that if (en ) n denotes the unit vector basis of c 0, there exists a sequence gn ∈ conv(f n , f n+1,...) such that for almost every ω, either the sequence (gn (ω) ⊗ en ) is weakly Cauchy in or it is equivalent to the unit vector basis of l 1. We then get a criterion for a bounded sequence to contain a subsequence equivalent to a complemented copy of l 1 in L 1(X). As an application, we show that for a Banach space X, the space L 1(X) has Pelczyniski's property (V*) if and only if X does.

Abstract: Let k be an algebraically closed field and A = kQ/I be a basic finite dimensional k-algebra such that Q is a connected quiver without oriented cycles. Assume that A is strongly simply connected, that is, for every convex subcategory B of A the first Hochschild cohomology H 1(B, B) vanishes. The algebra A is sincere if it admits an indecomposable module having all simples as composition factors. We study the structure of strongly simply connected sincere algebras of tame representation type. We show that a sincere, tame, strongly connected algebra A which contains a convex subcategory which is either representation-infinite tilted of type Ẽp, p = 6,7,8, or a tubular algebra, is of polynomial growth.

Abstract: Let μ be a finite positive Borel measure on the closed unit disc . For each a in , put where ƒ ranges over all analytic polynomials with f(a) = 1. This upper semicontinuous function S(a) is called a Riesz's function and studied in detail. Moreover several applications are given to weighted Bergman and Hardy spaces.

Abstract: Let G be a locally compact topological group. A number of characterizations are given of the class of compact groups in terms of the geometric properties such as Radon-Nikodym property, Dunford-Pettis property and Schur property of Ap(G), and the properties of the multiplication operator on PFp(G). We extend and improve several results of Lau and Ulger [17] to Ap(G) and Bp(G) for arbitrary p.

Abstract: We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on (0, oo) which is/7-convex for some/? > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if X is an r. i. space on (0,1) one can replace the hypotheses of r-convexity for some r>2byX^L2. We also show that if Y is an order-continuous Banach lattice which contains no com­ plemented sublattice lattice-isomorphic to l^ Xis an order-continuous Banach lattice so that £2 is not complementary lattice finitely representable in X and X is isomorphic to a complemented subspace of Y then X is isomorphic to a complemented sublattice of YN for some integer N. 1. Introduction. The study of the Banach space geometry of general rearrange­ ment-invariant Banach function spaces may be considered to originate with the work of Bretagnolle and Dacunha-Castelle on subspaces of Orlicz function spaces (3). A very important development in the theory was the publication of a systematic study of r. i. spaces by Johnson, Maurey, Schechtman and Tzafriri in 1979 (21). The appearance of this memoir revolutionized the subject. Since then, a number of authors have considered problems of classifying subspaces of certain special r. i. spaces; see (5), (6), (7), (8), (9), (13), (14), (17), (19), (20), (39), (40) for a variety of different results of this type. In general, most of the literature relates to the problem of embedding a Banach lattice X (either atomic or nonatomic) with additional symmetry conditions into an r. i. space Y, and the techniques used rely heavily on symmetrization. In (27), however, the second au­ thor considered the general problem of determining conditions when an order-continuous Banach lattice X could be complementary embedded in an order-continuous Banach lattice Y, minimizing the use of symmetry. The aim was to show that under certain hy­ potheses on X and Y one could deduce that X (or perhaps only a non-trivial band in X) would be lattice-isomo rphic to a complemented sublattice of Y. A number of such re­ sults were obtained (we refer for details to (27)); of course, the additional assumption that either X or Y is r. i. could still be used to obtain stronger results of this nature. In the final section of this paper (Section 8, which can be read independently of the remainder) we obtain a significant improvement of one of the results of (27) by showing that if X, Y are order-continuous separable Banach lattices, such that Y contains no complemented

Abstract: Let D be a divisor on a projectivized bundle over an elliptic curve. Numerical conditions for the very ampleness of D are proved. In some cases a complete numerical characterization is found.