Convolution of the Fourier coefficients of the Eisenstein-Maass series

The convolution is defined as the sum where for n≠0 and W₀,W₁ are arbitrary smooth functions. Question: how to express these sums in the form of the combinations of the N-th Fourier coefficients of the eigenfunctions of the automorphic Laplacian? The answer is given in terms of the bilinear form of the Hecke series associated with the eigenfunctions of the automorphic Laplacian and with regular cusp forms. The final identity may lead to a new possibility for the solution of the moment problem of the Riemann zeta-function.     

Congruence modularity implies the Arguesian identity

It is shown that if is any variety of algebras all of whose congruence lattices are modular, then the congruence lattice of every algebra in satisfies the Arguesian law.     

Fibrazioni di una classe di near-field regolari di dimensionet+1 sul nucleo

Il contenuto di questo lavoro consiste nel mostrare che le fibrazioni dei near-field regolari di dimensionet+1 sul nucleo , quando , si ottengono da fibrazioni regolari con una operazione di scambio fra alcuni sistemi di matrici, che generalizza il procedimento di sostituzione di regoli con regoli opposti di quadriche rigate nel caso di dimensione due sul nucleo.     

On the best convergence of trigonometric integrals

ОсНОВНОИ РЕжУльтАт Ё тОИ стАтьИ жАклУЧАЕт сь В слЕДУУЩЕМ. ЕслИ с ФИксИРОВАННыМr=2, 3,..., тО Дль тОгО, ЧтОБы ИМЕлО М ЕстО (*) гДЕ ДОстАтОЧНО ВыпОлНЕН ИЕ слЕДУУЩИх УслОВИИ: 1) ЕслИ $$1< \frac{{n_\nu + 1}}{{n_\nu }} = g_\nu \in N, \nu = 0,1,$$ тО Дль кАжДОгОΝ=0,1,... ИМЕ Ет МЕстО (**) 2) ЕслИ тО (***) $$n_{\nu + 1} \geqslant (2r - 1)n_\nu , \nu = 0,1,...$$ . ЕслИ И тО УслОВИь (**), (***) ьВльУтсь тАкжЕ НЕОБхОДИМыМИ Д ль (*).     

On a characterization of finite dimensional real linear spaces

LetX be a real linear space; if is a linear topology onX, let denote the class of all bounded with respect to subsets ofX. In this paper it is shown that the spaceX is algebraically finite dimensional if and only if the class of all convex, absorbing and radially bounded subsets ofX is included in the intersection of all , where runs the set of all linear topologies onX.     

On a sublattice of the lattice of congruences on a θ-regular semigroup

Let S be a regular semigroup. The lattice of all idempotent-separating congruences on S and the lattice of all group congruences on S are both modular sublattices of the full lattice of congruences on S. It is evident that the set theoretical union of these two sublattices, (S), is also a sublattice of the full lattice of congruences on S. It is natural to ask: Under what conditions is the sublattice (S) modular? In this paper we obtain a necessary and sufficient condition for the sublattice (S) to be modular when S is what we call a θ-regular semigroup. Bisimple ω-semigroups and simple regular ω-semigroups are θ-regular semigroups and so this paper extends the work of Munn [5] and Baird [1].     

On inductive limits of measure spaces

We introduce a category of (topological) measure spaces in which inductive limitis exist and where the Banach spaces and (1≤p≤+∞) are isometric for arbitrary inductive systems of (topological) measure spaces.     

Les F-reguliers a gauche

1. The concept of left F-regular semigroups was first defined by Batbedat at the Oberwolfach meeting in 1981. It generalizes the notion of F-regular semigroup introduced by Edwards [4], itself a generalization of the F-inverse semigroups defined by McFadden/O’Carroll [6]
2. In the present paper we generalize the results of [4] and [6] by defining two preorders and ? on a monoid S with a distinguished band E, as follows: iff x=ay for some a∈E xδy iff x=yb for some b∈E
3. When S is regular orthodox and E=E(S), is the preorder of [1] p. 29 and is the order of [1] p. 31 (the order of [4]): in fact is the natural partial order introduced by Nambooripad [7].
4. In b), we define the relation Σ on S: xΣy iff exe=eye for some e∈E Then we consider the congruence σ generated by Σ.
5. DEFINITION. S is left F_E-monoid if each σ-class contain a greatest element with respect to .
6. PARTICULAR CASES. When S is regular, S is left F_E-regular. When S is regular orthodox and E=E(S), S is left F-regular.
7. We describe the structure of left F-regular semigroups like in [1], [2], [4] and [6]. Note that every left F-regular semigroup is a gammasemigroup [3]
8. Particular Cases (gamma morphism) and applications (congruences).

     

Un teorema sulla rappresentazione degli integrali

Let be a De Possel differentiation basis in a complete measure space , with μ≥0, μ(X)<+∞; letB be a Banach space and . When the F′ exists μ-a.e. onX, we prove that for eachp>0, the μ-integral of‖F′‖ ^p is the lower-bound of a class ofp-variations.     

A generalization of a theorem of Kruskal

LetA be a set ofk-subsets of {1,...,n} with . We determine the minimal cardinality of thel-shadow ofA. This theorem generalizes a theorem of Kruskal [10], Katona [8], Lindström [11] and other which gives a solution for the problem without the condition . Furthermore we give a necessary and sufficient condition for the uniqueness of the solution in the KKL theorem.     

On some classes of contact metric manifolds

We define four new classes of contact metric manifoulds using Tanaka connection and Jacobi operators. We prove that a contact metric manifold with the structure vector field ξ belonging to thek-nullity distribution is contact metric locally ?-symmetric (in the sense of D. B. Blair) if and only if the manifold is a and space. Also, we prove that a 3-dimensional contact metric and is locally ?-symmetric (in the sense of D. E. Blair) and give counter-examples of the converse.     

Characterization of joint ergodicity for non-commuting transformations

The study of jointly ergodic transformations, begun in [2] and [1], is continued. The main result is that, ifT ₁,T ₂, …,T _s are arbitrary measure preserving transformations of a probability space (X, ?,μ), then , if and only if the following conditions are satisfied:

1. T ₁×T ₂×…×T _s is ergodic.
2. .

     

О разложениях в ряд ы о бобщенно-абсолютно-м онотонных функций

In an earlier paper [1] the notion of the so-called 〈?, GL_J>-absolutely monotonie functions was introduced, where ?≧1, {λ_{k k=0} ^∞ is an arbitrary non-increasing sequence of positive numbers. It was found that the condition \(\sum\limits_{\lambda _{k > 0} } {\lambda _k^{ - 1} } = + \infty \) is necessary in order to have the series expansion for any function f(x)∈〈?, λ_j). HereL ^k/? f/(x) are special integro-differential operators of fractional order, is a system of functions associated with the Mittag-Leffler type functions \(E_\varrho (z;\mu ) = \sum\limits_{k = 0}^\infty {z^n /\Gamma (\mu + \kappa /\varrho )} \) and with the sequence {λ_k}. In the present paper it is proved (in particular, see Theorem 3.2) that the expansion (*) is valid almost everywhere on (0,l) if ∑ λ _k ^?1 =+∞. This result contains, as a special case (when ?=1 and λ_k=0,k≧0) the known theorem of S. N. Bernstein on absolutely monotonic functions.     

Interpolation,compactness and JEP in soft model theory

Let be the following statement: “for any infinite regularκ, for any uniform ultrafilterD onκ,D isλ-descendingly incomplete for all infiniteλ”. is weaker than ?0^#. Assuming we prove the following: letL be a logic in which the class of sentences of typeτ is a set if so isτ; then: (I)L is compact iffL has JEP; (II)L satisfies Robinson Consistency Theorem iffL is compact and satisfies Craig Interpolation theorem; (III) if, in addition,L is single-sorted, thenL satisfies Robinson Consistency Theorem iffL has JEP^#. JEP (resp. JEP^#) are the natural generalizations for logicL of the familiar Joint Embedding Property of elementary (resp. complete) embeddings in first order logic. As a corollary, we characterize first order logic as the only logic having Löwenheim number equal toω together with JEP.     

Ein zerlegungssatz für P(ϰ)

We shall prove the following partition theorems:

1. For every setS and for each cardinal ? ≥ ω, |S| ≥ ? there exists a partitionT: [S]^? → 2^? such that for every pairwise disjoint familie and everyα < 2^? there exists a set
2. Suppose ? ≥ ω, 2 ^{andS an arbitrary set, 2|S| ≤ (2?)+ω Then there exists a partitionT: P(S) → 2? such that for every pairwise disjoint family and everyα < 2? there exists a set Both theorems will give partial answers to an Erd?s problem.}

     

The space BMO and strong means of Fourier series

пУстьS _k (f,x) — ЧАстНАь сУ ММА РьДА ФУРьЕ ФУНкцИ Иf пО тРИгОНОМЕтРИЧЕскОИ сИстЕМЕ,s _k (f,x) — ЧАстНАь сУММА сО пРьжЕННОгО РьДА. Дль \(\Delta _k^n = \left[ {\frac{n}{n},\frac{{k + 1}}{n}} \right)\) , гДЕk=0, 1, ...,n?1, пОлОжИМ , ЕслИt?δ _k ⁿ И , ЕслИt?[0, 1)δ _k ⁿ . пОкАжАНО, ЧтО ОпЕРАтО Ры ИМЕУт слАБыИ тИп (1,1). РАссМОтР ЕН РьД слЕДстВИИ О пОВ ЕДЕНИИ сИльНых сРЕДНИх РьДА ФУРьЕ сУММИРУЕМОИ ФУНкцИИ.     

Nonlocal problems for one class of nonlinear operator equations that arise in the theory of sobolev type equations

Let , be Hilbert spaces forming a sequence of compact imbeddingsH ₃ ?H ₂ ?H ₁ ?H ₀. Consider the nonlinear equation in H₂ and suppose that conditions (8)–(12) and (15) hold for the operators A and K(u) and the external force F(t). Four nonlocal problems (cf. 1–4) are studied for such equations. Examples are given [cf. (2)–(6)] for nonlinear dissipative equations of Sobolev type that are reducible to an abstract non-linear equation [cf. (7)–(12), (15)].     

Classi di isomorfismo delle cubiche diF q

LetF _q (q=p^r) be a field of characteristicp>3 andA the set of all elliptic cubic curves overF _q having a given absolute invariantj. Furthermore let ≈be the following equivalence relation: « if and only if and F_q are isomorphic overF _q as abelian varieties». The aim of this paper is to study the equivalence classes inA, induced by ≈, and the Frobenius' traces of the cubic curves belonging to different subclasses ofA.     

On the strong approximation by the (C, α)-means of Fourier series. I

Статья продолжает ис следования Г. Суноути, Л. Лейндлера и В. Ленског о; она посвящена изучению средних вида . Здесь α> — 1/2 и рα> — 1. Для а>0 полностью иссл едован случай неотри цательной, регулярной матрицы {t _nk } и классаH ^ω (ω — модуль не прерывности). При 0>а> ?1/2 получены результаты для весьма широкого клас са матриц. Доказано, чт о в каждом случае порядки указа нных величин для функций изH ^ω совпа дают с . Кроме того, устанавли вается, что не существ ует естественных обобще ний этих утверждений на классыW ^r H ^ω (r≧1). Из результатов стать и вытекают решения не которых ранее поставленных з адач.