Symmetric balanced ternary designs with ϱ1 = 1 or 2

Summary We prove the following two non-existence theorems for symmetric balanced ternary designs. If ₁ = 1 and 0 (mod 4) then eitherV = + 1 or 4₂ – + 1 is a square and (4₂ – + 1) divides ² – 1. If ₁ = 2 thenV = ((m + 1)/2) ² + 2,K = (m ² + 7)/4 and = ((m – 1)/2)² + 1 wherem 3 (mod 4). An example belonging to the latter series withV = 18 is constructed.     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

Relaxation of a Quadratic Functional Defined by a Nonnegative Unbounded Matrix

We study the lower semicontinuous envelope in L^p(), F, of a functional F of the form F(u)=A uudx where A=A(x) is not strictly elliptic and not bounded. We prove that F; may also be written as F;(u)= Buudx with B=AP A for a matrix P which is the matrix of an orthogonal projection. In the one-dimensional case, we characterize the domain of F and we explicit the matrix P.     

Invarianz gewisser Operatorenklassen unter nichtkommutativen ergodischen Mitteln

Let be a group of *-automorphisms on the algebra of bounded linear operators on a complex Hilbert space H. Then the strongly closed convex hull of the orbit of any compact operator under consists of compact operators. The same is true if one replaces compact by nuclear, Hilbert-Schmidt or positive Fredholm. We further discuss these results in the framework of the noncommutative mean ergodic theorem of KOVACS and SZ#x00FC;CS and formulate an analogous theorem for the algebra of compact operators on a complex Hilbert space.

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Gefördert von der Deutschen Forschungsgemeinschaft im Rahmen des Forschungsvorhabens Ko 506/1.     

Maximal inequalities,convexity inequality,and their duality. II

, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .     

On an application of infinitely divisible distributions to quadrature problems

— - , .     

On the solution of a generalized Schrödinger-type equation

Lu(t)+(u,F)g(t)=f(t), tS. , ( F, g). .

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The authors wish to thank Professor Yu. A. Rozanov for his help and discussions.     

Beitrag zur Reduktion des Entscheidungsproblems auf Klassen von Hornformeln mit kurzen Alternationen

Ohne Zusammenfassung Zusatz bei der Korrektur: Ein vollständiger und korrekter Beweis für die Entscheidbarkeit der eingangs angeführten Aanderaaschen Klasse ((0, ), (, , ...)) erscheint demnächst im JSL (S.O. Aanderaa/H.R.Lewis: Prefix classes of Krom formulas). Ebendort wird auch die Reduktionstypeneigenschaft für ((0, ), (0, 0, )) und ((0, )), (0, 0, )) nachgewiesen, während ((0, ), (, )) sich als entscheidbar herausgestellt hat (s. E. Börger: Eine entscheidbare Klasse von Kromformeln. ZMLG 19 (1973), 117–120.) Der Kromsche Reduktionstyp konnte mittlerweile einerseits zu ((0, ), (0, 4)) verschärft werden (s. D. Rödding, E. Börger: The undecidability of (0, 4)-formulae with binary disjunctions, vorgetragen auf dem Logic Coll. Bristol 1973, ein abstract erscheint im JSL), andererseits kündigt H.R.Lewis die Reduktionstypeneigenschaft für ((0, ), (0, 1)) an (s. H.R.Lewis: Krom formulas with one dyadic predicate letter. Notices AMS 20, 5 (1973) A-500, abstr. no. 73T-E78.)Dieser Aufsatz geht aus der Dissertation [2] hervor, die dem Fachbereich Mathematik der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Münster im Sommersemester 1971 vorgelegt worden ist. Die Ergebnisse stammen aus dem Wintersemester 1970/71. Eine Ankündigung der hauptsächlichen Resultate ist in den Notices of the American Mathematical Society 19, 2 (1972) A-333 unter der abstract no. * 72T-E24 erschienen.     

A generalized integral with applications to trigonometric series

, . . .

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The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee.     

On the stability of the transport equation

We consider boundary value problems associated with the equation T=–A in a Hilbert Space, where T and A are bounded, self adjoint, injective, and A has a bounded inverse. We discuss the stability of the solution when A is perturbed by a self adjoint operator.     

Асимптоический Анализ Распределения Статистики Диксона

. u 60-u u     

On the type of spectral operators and the non-spectrality of several differential operators on Lp

A spectral operator, not necessarily bounded, which is the infinitesimal generator of a strongly continuous group of operators {U(t)|t} where U(t) = (|t|^K), is of type k N_o, i.e. T = S + N, where S is spectral of scalar type, N is bounded, N^k+1 = O and S and N are commuting. This result yields a simple proof of the non-spectrality of certain differential operators on L^p, p 2, which are known to be selfadjoint for p = 2.     

A certain class of functions that are univalent in an annulus

In the class F₁ of functions f(), regular and univalent in the annulus ={<||<1} and satisfying the conditions ¦f()¦ < 1 and f() 0 for , ¦f()¦=1 ¦¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f for an arbitrary fixed point A. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985.     

Spectral parameter asymptotics of the Weyl solutions of Sturm-Liouville equations

In the paper one investigates the dependence of Weyl's solution ,)=c(,)+n()s(,) of the Sturm-Liouville equation y+q()y=²y on the spectral parameter . Under the condition that the potential q is bounded from below and q()exp(c₀+c[in1 ¦¦), it is proved for {ie217-01} for any positive values and A. If q()>1 and {ie217-02} for all >0, then in the semiplane >0 the Weyl solution (, ) is obtained from the Weyl solution (,x) is obtained from the Weyl solution e^ix with zero potential, with the aid of a generalization of B. Ya Levin's transformation operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 184–206, 1989.I express my sincere gratitude to L. A. Pastur and I. V. Ostrovskii for valuable advice and discussions.     

Spectral properties of certain operators on Hardy spaces of planar regions

If G is any region in the complex plane and H^P (G), 1p, denotes the Hardy space of analytic functions on G, then the principal aim of this paper is to present the spectral properties of the multiplication operators M defined on H^P(G) by Mf=f, where is any bounded analytic function on G. In order to do this, the speccial case in which G is bounded and (z)=z is studied in detail. In addition an operator called the truncation operator that is not a multilication operator and acts on the Hardy spaces of regions of the form /K for a compact set K is studied.Dedicated to the memory of my brotherThis research was partially supported by National Science Foundation grant MCS 83-204-26.     

Some extensions of the Hewitt-Savage zero-one law

Summary Let denote the class of infinite product probability measures = ₁× ₂× defined on an infinite product of replications of a given measurable space (X, A), and let denote the subset of for which (A) =0 or 1 for each permutation invariant event A. Previous works by Hewitt and Savage, Horn and Schach, Blum and Pathak, and Sendler (referenced in the paper) discuss very restrictive sufficient conditions under which a given member , of belongs to . In the present paper, the class is shown to possess several closure properties. E.g., if and _{0 n} for some n 1, then ₀× ₁× ₂×.... While the current results do not permit a complete characterization of they demonstrate conclusively that is a much larger subset of than previous results indicated. The interesting special case X={0,1} is discussed in detail.Research supported by the National Science Foundation under grant No. MCS75-07556     

Orders of one-sided approximations of functions inL p -metric

. L _p , 0<p<, . , f, {E _n (f) _p } ₁ p>0 .

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The author expresses his thanks to S. B. Stekin for the attention he has paid to this work.     

Free Wishart Processes

Using a matrix approach, we define free Wishart processes of parameter > 0 and prove a free additivity property and invertibility for > 1. For 1, we show that a free Wishart process is a solution of a SDE of square Bessel process type, driven by a free complex Brownian motion. In the case > 1, we establish existence and uniqueness of a strong solution of such a SDE.     

Existence of quadrature surfaces for positive measures with finite support

Let be a positive measure with finite support in ⁿ (n2). Then we show that there is a bounded open set , containing the support of , whose single-layer potential coincides with the potential of outside .