Adjoints of slant Toeplitz operators

In this paper, we will use the Birkhoff's ergodic theorem to do some finer analysis on the spectral properties of slant Toeplitz operators. For example, we will show that if is an invertibleL function on the unit circle, then almost every point in (A ^* ) is not an eigenvalue ofA ^* . More specifically, we will show that the point spectrum ofA ^* is contained in a circle with positive radius.     

Perturbation des résolvantes et représentation des mesures excessives

Résumé Etant donnée une résolvante V=(V )_>0 sous-markovienne sur un espace mesurable (X, B) de noyau initial V propre; on étudie alors le balayage des mesures surmédianes au moyen de la résolvante perturbée V de V par une function mesurable positive bornée sur X.Dans le cas où (X, E _v) est un espace de balayage, on montre que toute mesure excessive vérifiant , s'écrit d'une manière unique sous la forme =V où est une mesure positive sur X.     

Interpolation theorems for a family of spanning subgraphs

Let G be a graph with order p, size q and component number . For each i between p – and q, let be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H is an adjacent edge transformation (AET) implies |(H)-(H^')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M _j() and m _j() be the invariants defined by . It is proved that both M _p–() and m _p–(;) interpolate over , if is continuous with respect to AET, and that M _j() and m _j() interpolate over , if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized.     

On lower bounds in radial basis approximation

We investigate the approximation by manifolds _n() generated by linear combinations of n radial basis functions on R^d of the form (|–a|), where is the thin-plate spline type function. We obtain exact asymptotic estimates for the approximation of Sobolev classes W^r(B^d) in the space L(B^d) on the unit ball B^d. AMS subject classification 41A25, 41A63, 65D07, 41A15     

On the decomposition theorem for meromorphic Fredholm resolvents

In this note results of B. Gramsch and W. Kaballo [8] on the decomposition of meromorphic (semi-) Fredholm resolvents are sharpened. A condition on an Orlicz function is given, under which the singular part in this decomposition can be chosen meromorphic inN , the ideal of -nuclear operators. Then the necessity of this condition is studied. Moreover, it is shown that for the rather steep Orlicz functions relevant to this question,N equalsS , the ideal of -approximable operators.Dedicated to Professor Albert Schneider on the occasion of his 60 ^th birthdayresearch supported by a grant from DAAD     

Uniqueness of Nelson's Diffusions II: Infinite Dimensional Setting and Applications

Under mild condition on the modulus = of the time independent wave function , we prove that the generalized Schrödinger operator = + 2 (, ·)/ (or the generator of Nelson's diffusion) defined on a good space of test-functions on a general Polish space, generates a unique semigroup of class (C _o) in L ¹. This result reinforces the known results on the essential Markovian self-adjointness in different contexts and extends our previous works in the finite dimensional Euclidean space setting. In particular it can be applied to the ground or excited state diffusion associated with an usual Schr\"odinger operator , and to stochastic quantization of several Euclidean quantum fields.     

Nonlinear programming,approximation, and optimization on infinitely differentiable functions

A nonnegative, infinitely differentiable function defined on the real line is called a Friedrichs mollifier function if it has support in [0, 1] and ₀ ¹ (t)dt=1. In this article, the following problem is considered. Determine _k =inf ₀ ¹ |^(k)(t)|dt,k=1, 2, ..., where ^(k) denotes thekth derivative of and the infimum is taken over the set of all mollifier functions , which is a convex set. This problem has applications to monotone polynomial approximation as shown by this author elsewhere. The problem is reducible to three equivalent problems, a nonlinear programming problem, a problem on the functions of bounded variation, and an approximation problem involving Tchebycheff polynomials. One of the results of this article shows that _k =k!2^2k–1,k=1, 2, .... The numerical values of the optimal solutions of the three problems are obtained as a function ofk. Some inequalities of independent interest are also derived.This research was supported in part by the National Science Foundation, Grant No. GK-32712.     

Analysis of a class of fractional programming problems

We propose a solution strategy for fractional programming problems of the form max _xx g(x)/ (u(x)), where the function satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max _xx g(x) + u(x), where is an exogenous parameter. The proposed strategy combines fractional programming andc-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.     

Résolution numérique des grands systèmes différentiels linéaires

Sommaire La solution stricte d'un système différentiel linéaire à coefficients constants [d /d t] = [A] [] + [f (t) ] est donnée par: [ (t)]= [e^At] [ (0) ] + f [e^A(t–)] [f (T) ] d .Cette relation, utilisée dans une méthode de pas à pas, permet le calcul de [(t+u)] en fonction de [(t)]. La mise en oeuvre numérique de cette formule nécessite le calcul de [e^A] et de l'intégrale de matrice du second membre.Le sujet de cette étude est la mise au point de techniques d'approximation permettant le calcul effectif de [e ^Aµ] et de l'intégrale de matrice par des méthodes qui peuvent s'adapter en particulier aux systèmes différentiels à très grand nombre d'inconnues, qui apparaissent par exemple dans l'approximation par discrétisation enx ety, de l'équation aux dérivées partielles, dite de la chaleur.     

Approximate first-order and second-order directional derivatives of a marginal function in convex optimization

Given a convex functionf: ^p × ^q (–, +], the marginal function is defined on ^p by (x)=inf{f(x, y)|y ^q }. Our purpose in this paper is to express the approximate first-order and second-order directional derivatives of atx ₀ in terms of those off at (x ₀,y ₀), wherey ₀ is any element for which (x ₀)=f(x ₀,y ₀).The author is indebted to one referee for pointing out an inaccuracy in an earlier version of Theorem 4.1.     

Equivalence Bimodule Between Non-Commutative Tori

The non-commutative torus C ^*(ⁿ,) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over S with fibres isomorphic to C ^*n/S, ₁) for a totally skew multiplier ₁ on ⁿ/S. D. Poguntke [9] proved that A is stably isomorphic to C(S) C(^*( Zⁿ/S, ₁) C(S) A M_kl( C) for a simple non-commutative torus A and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an A-C(S) A-equivalence bimodule.     

Implicit elliptic boundary-value problems with discontinuous nonlinearities

Let be a bounded domain in ⁿ (n3) having a smooth boundary, let be an essentially bounded real-valued function defined on × ^h, and let be a continuous real-valued function defined on a given subset Y of Y ^h. In this paper, the existence of strong solutions u W ^2,p (, ^h) W _o ^1,p (n/2<p<+) to the implicit elliptic equation (–u)=(x,u), with u=(u₁, u₂, ..., u_h) and u=(u ₁, u ₂, ..., u _h), is established. The abstract framework where the problem is placed is that of set-valued analysis.     

Curves and 0-cycles on projective surfaces

LetC be a smooth curve with ag _n ¹ , i.e. a linear system of dimension 1 and degreen, lying on a smooth projective surfaceS. Let :S P ^N be the map associated to the line bundleK _S +[C] and letD be a general divisor of the given linear systemg _n ¹ . LetV be the linear space spanned by the image ofD through . We study the case in whichn:=dimV=1 and in general we discuss the case in whichn is small. The starting point is an analysis of the adjunction map using Bogomolov-Reider-Serrano techniques; several results from curve theory are also needed.     

On Dirichlet Processes Associated with Second Order Divergence Form Operators

Let be a d - dimensional Markov family corresponding to a uniformly elliptic second order divergence form operator. We show that for any quasi continuous in the Sobolev space the process (X) admits under P ^x a decomposition into a martingale additive functional (AF) M and a continuous AF A of zero quadratic variation for almost every starting point x if q=2, for quasi every x if q>2 and for every if is continuous, d=1 and or d>1 and q>d. Our decomposition enables us to show that in the case of symmetric operator the energy of A equals zero if q=2 and that the decomposition of (X) into the martingale AF M and the AF of zero energy A is strict if for some q>d. Moreover, our decomposition provides a probabilistic representation of A .     

Comparing different classes of absolutely summing multilinear operators

Let C denote the composition operator defined on the standard Hardy spaces H^p as where is an analytic self-map of the unit disk in the complex plane. In this paper we discuss those invariant subspaces of C in H^p which are invariant under the shift operator, We restrict our attention to the case where is an inner function. Our main result characterises these invariant subspaces. We also consider C when restricted to such an invariant subspace and we describe the structure of the operator and find a formula for the essential spectral radius.Received: 27 January 2004     

Linear cyclic codes of wordlength v over GF(q s ) which are also linear cyclic codes of wordlength sv over GF(q)

Any nonsingular linear transformation : GF(q^s) GF(q^s) can be used to treat a linear cyclic code of wordlength v over GF(q^s) as a linear code () of Wordlength sv over GF(q). This paper determines those linear cyclic codes and transformations for which the resulting linear code () is also cyclic.     

Groups with Largely Splitting Automorphisms of Orders Three and Four

A subset X of a group G is said to be large (on the left) if, for any finite set of elements g₁,l... ,g_kin G, an intersection of the subsets g_iX=g_imid x in X is not empty, that is, limits_{i=1} ^{k}g_iX . It is proved that a group in which elements of order 3 form a large subset is in fact of exponent 3. This result follows from the more general theorem on groups with a largely splitting automorphism of order 3, thus answering a question posed by Jaber amd Wagner in [1]. For groups with a largely splitting automorphism of order 4, it is shown that if His a normal -invariant soluble subgroup of derived length d then the derived subgroup [H,H] is nilpotent of class bounded in terms of d. The special case where =1 yields the same result for groups that are largely of exponent 4.     

Quasi-coherence of Hardy spaces in several complex variables

In this paper, we prove that the Hardy spaceH ^p (), 1p<, over a strictly pseudoconvex domain in ⁿ with smooth boundary is quasi-coherent. More precisely, we show that Toeplitz tuplesT with suitable symbols onH ^p () have property (). This proof is based on a well known exactness result for the tangential Cauchy-Riemann complex.     

n-th roots of a non-negative operator. Conditions for uniqueness

In the present paper we study which restrictions must be imposed on the n-th roots of certain non-negative closed operators A on a Banach space so that these roots are unique.Counterexamples are given to show that the two results on this subject in the previous literature are incorrect.Finally, we obtain an explicit formula relating the canonical root A^1/n to another given non-negative n-th root B, and this allows us to establish the conditions for a given element to yield the same value by both roots. This point of view, which had not been considered up to now, provides simple conditions for global uniqueness that need only to be checked on the subspaces D(A)=_n1D(Aⁿ) and R(A)=_n1R(Aⁿ).     

On almost complete intersections

Let R be a local ring such that R=S/I where S is a regular local ring and I is a prime ideal of height r. In this paper it is shown that if I is minimally generated by r+1 elements, then there exists an R-homomorphism : K_RR^r+1 such that is an injection and R^r+1/(K_R)I/I² where K_R:=Ext _S ^r (R,S) the canonical module of R. Moreover, in case where S is a locality over a perfect field k, it is also shown that if R is Cohen-Macaulay and I² is a primary ideal, then the homological dimension of the differential module _R/k is infinite.The author wishes to thank his colleague Mr.Y.Aoyama for valuable discussions in connection with this subject.