Waterman classes and spherical partial sums of double Fourier series

f(x,y) ₀BV(T²), ={1/n} _n=1 .

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Dedicated to Professor Károly Tandori, the outstanding mathematician and academician on his seventieth birthday

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This work was done under the financial support of the Russian Foundation for Fundamental Scientific Research, Grant 93-01-00240.     

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.     

General Solution for Hamiltonians with Extended Cubic and Quartic Potentials

In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases 1:6:1 and 1:6:8.     

Integrability of multiple Walsh series and Parseval's formula

f(x,y) _jk . , {c _jk} , f(x, )(, ) [0,1)х[0,1) , - (0,0). , , f, - f. , , , [1] . . - [5] [6].

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This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026.     

Differentiation of fractional order onp-groups,approximation properties

G- p- . [5] - (G) L _r(G) (1r<), . . , - . , , , . . , X. , . (. [1], [2] [4]).     

Onp-Helson sets in R n

p- . E R ⁿ -, f () _p(R ⁿ)., ER ⁿ 2nq ₀, E— - q ₀(q ₀-1). : q₀>2 n1 E R ⁿ 2nq ₀, p- p<₀. , f-[-, ]ⁿ, f A _p(R ⁿ) , _p([-, ]ⁿ) (1 << ).     

On the convergence of Fourier series in the metric ofL 1

L ¹ .      

Arithmetic properties of the Markov function for the Jacobi weight

. . .     

C 1 changes of variable: Beurling-Helson type theorem and Hörmander conjecture on Fourier multipliers

We prove that if aC ¹ smooth change of variable : generates a bounded composition operatorff° in the spaceA _p()=L ^p ,p2, then is linear (affine).We also prove that for a nonlinearC ¹ mapping , the norms of exponentialse ⁱ as Fourier multipliers inL ^p () tend to infinity (,||). In both results the condition C ¹ is sharp, it cannot be replaced by the Lipschitz condition.     

A note on rational approximation rate for Müntz system {x λn } with λ n ↘ 0

[Zho2] {x ⁿ } , _n 0 n .

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Supported in part by an NSERC Postdoctoral Fellowship and a CRF grant of University of Alberta.     

О предельном распределении для сумм независимых слууайных велиуин на бикомпактных коммутативных топологиуеских группах

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Embeddings of Lorentz—Marcinkiewicz spaces with mixed norms

X(Y) f -:X(Y)={fM(×): f_{X(Y)=f(x,.)YX<} . =(0, ), M (×) — , ×, X, Y, Z— . X(Y) Z(×).     

A two‐level queueing network model with blocking and non‐blocking messages

We analyze a novel twolevel queueing network with blocking, consisting of N level1 parallel queues linked to M level2 parallel queues. The processing of a customer by a level1 server requires additional services that are exclusively offered by level2 servers. These level2 servers are accessed through blocking and nonblocking messages issued by level1 servers. If a blocking message is issued, the level1 server gets blocked until the message is fully processed at the level2 server. The queueing network is analyzed approximately using a decomposition method, which can be viewed as a generalization of the wellknown twonode decomposition algorithm used to analyze tandem queueing networks with blocking. Numerical tests show that the algorithm has a good accuracy.     

Characterization of regular singular linear systems of difference equations

This paper deals with linear systems of difference equations whose coefficients admit generalized factorial series representations atz=. We are concerned with the behavior of solutions near the pointz= (the only fixed singularity for difference equations). It is important to know whether a system of linear difference equations has a regular singularity or an irregular singularity. To a given system () we can assign a number , called the Moser's invariant of (), so that the system is regular singular if and only if 1. We shall develop an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations to an irreducible form. The computation ot the number can be done explicitly from this irreducible form.     

Feller Processes Generated by Pseudo-Differential Operators: On the Hausdorff Dimension of Their Sample Paths

Let {X _t} _t0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇⁿ|q(Ç,)|c(1=)()) for some fixed continuous negative definite function (). The Hausdorff dimension of the set {X _t:tE}, E [0, 1] is any analytic set, is a.s. bounded above by dim E. is the Blumenthal–Getoor upper index of the Levy Process associated with ().     

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.     

Stability and uniqueness of the solution of the inverse kinematic problem of seismology in higher dimensions

The following inverse kinematic problem of seismology is considered. In the compact domain M of dimension ,2 with the metric, we consider the problem of constructing a new metricdu=nds according to the known formula where ,M and K_, is the geodesic in the metric du, connecting the points , . One proves uniqueness and one obtains a stability estimate, where the refraction indices n₁, n₂ are the solutions of the inverse kinematic problem, constructed relative to the functions ₁, ₂, respectively, is the differential form on M×Mwhere =₂–₁,.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 84, pp. 3–6, 1979.     

Characterization,structure and analysis on abelian ℒ∞ groups

An abelian topological group is an group if and only if it is a locally -compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian groupG is topologically isomorphic to G ₀ where ₀ andG ₀ is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra,L ₁-algebra, Fourier transforms of abelian groups are given and their properties are studied.     

On Interpolation Sequences of One Class of Functions, Analytic in the Half-Plane

A new criterion of solvability of the interpolation problem f( _n )=b_n in the class of functions f, analytic in the right half-plane and such that there exists c ₁(0;+) such that |f(z)|c ₁exp((c₁|z|)) for all z , where is a positive increasing continuous differentiable function on [0;+), for which (t)+ as t+ and there exists c ₂(0;+) such that

On Interpolation of the Fourier Maximal Operator in Orlicz Spaces

Let and be positive increasing convex functions defined on [0, ). Suppose satisfies the 2-condition, that is, (t)2 (C1t) for sufficiently large t, and has some nice properties. If -1(u)log(u+1) C2-1(u) for sufficiently large uthen we have S*(f) L CfL for all f L ([-, ])where S*(f) is the majorant function of partial sums of trigonometric Fourier series and fL is the Orlicz norm of f. This result is sharp.