Complete convergence theorems for L-mixingales

Sufficient conditions for the complete convergence for the partial sums and the random selected partial sums of L^p-mixingales are given. Necessary conditions are also discussed.     

On subspaces of non-commutative Lp-spaces

We study some structural aspects of the subspaces of the non-commutative (Haagerup) L_p-spaces associated with a general (non-necessarily semi-finite) von Neumann algebra . If a subspace X of contains uniformly the spaces ?_pⁿ, n?1, it contains an almost isometric, almost 1-complemented copy of ?_p. If X contains uniformly the finite dimensional Schatten classes S_pⁿ, it contains their ?_p-direct sum too. We obtain a version of the classical Kadec-Pe?czyński dichotomy theorem for L_p-spaces, p?2. We also give operator space versions of these results. The proofs are based on previous structural results on the ultrapowers of , together with a careful analysis of the elements of an ultrapower which are disjoint from the subspace . These techniques permit to recover a recent result of N. Randrianantoanina concerning a subsequence splitting lemma for the general non-commutative L_p spaces. Various notions of p-equiintegrability are studied (one of which is equivalent to Randrianantoanina's one) and some results obtained by Haagerup, Rosenthal and Sukochev for L_p-spaces based on finite von Neumann algebras concerning subspaces of containing ?_p are extended to the general case.     

q-Dedekind type sums related to q-zeta function and basic L-series

The main purpose of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q-L-function. In particular, by using these generating functions, we will construct new generating functions which produce q-Dedekind type sums and q-Dedekind type sums attached to Dirichlet character. We also give the relations between these sums and Dedekind sums. Furthermore, by using *-product which is given in this paper, we will give the relation between Dedekind sums and q-L function as well.     

L-topological vector spaces and families of L-fuzzy pseudo-norms

In this paper, the concept of a family of L-fuzzy pseudo-norms on vector spaces is proposed and the characterization of L-vector topologies in terms of a family of L-fuzzy pseudo-norms is presented. As applications of the characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-sets in L-topological vector spaces are investigated.     

Kernel systems on L-ordered sets

This paper presents fuzzy versions of kernel operators and kernel systems on L-ordered sets and establishes a one-to-one correspondence between them.     

L-fuzzy Q-convergence structures

In this paper, we construct a topological category of pretopological L-fuzzy Q-convergence spaces, which contains the category of topological L-fuzzy Q-convergence spaces as a bireflective full subcategory. Considering the connections with L-fuzzy topology, it is proved that the category of topological L-fuzzy Q-convergence spaces is isomorphic to the category of topological L-fuzzy quasi-coincident neighborhood spaces, and the latter is isomorphic to the category of L-fuzzy topological spaces. Moreover, we find that our pretopological L-fuzzy Q-convergence spaces can be characterized as a kind of L-fuzzy quasi-coincident neighborhood spaces, which is called strong L-fuzzy quasi-coincident neighborhood space.     

On some functional relations between Mordell-Tornheim double L-functions and Dirichlet L-functions

In the past decade, many relation formulas for the multiple zeta values, further for the multiple L-values at positive integers have been discovered. Recently Matsumoto suggested that it is important to reveal whether those relations are valid only at integer points, or valid also at other values. Indeed the famous Euler formula for ζ(2k) can be regarded as a part of the functional equation of ζ(s). In this paper, we give certain analytic functional relations between the Mordell-Tornheim double L-functions and the Dirichlet L-functions of conductor 3 and 4. These can be regarded as continuous generalizations of the known discrete relations between the Mordell-Tornheim L-values and the Dirichlet L-values of conductor 3 and 4 at positive integers.     

Maximal element theorems in product FC-spaces and generalized games

Let I be a finite or infinite index set, X be a topological space and (Yi,{φNi})_i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i∈I, let be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}_i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

Coreflective hull of finite strong L-topological spaces

This paper is concerned with the interaction between the logic features of the table of truth values and categorical properties of L-topological spaces and L-co-topological spaces. On one hand, it is shown that for each unital quantale L, the category of Alexandroff strong L-co-topological spaces is the coreflective hull of finite strong L-co-topological spaces. On the other hand, in the case that the quantale L is the unit interval [0,1] equipped with a continuous t-norm, it is shown that the category of Alexandroff strong [0,1]-topological spaces is the coreflective hull of finite strong [0,1]-topological spaces if and only if the continuous t-norm is an ordinal sum of the ?ukasiewicz t-norm whose set of idempotent elements is a well-ordered subset of [0,1] under the usual order.     

Multivariate basic hypergeometric series associated to root systems of type Am

In previous paper [Ann. Comb. 4 (2000) 347-373], we established and proved two new q-beta integrals and two multivariate basic hypergeometric series associated with the root system of A_m. In this paper we give a detailed proof of the multivariate basic hypergeometric series obtained in [Ann. Comb. 4 (2000) 347-373].     

Noncommutative localization in algebraic L-theory

Given a noncommutative (Cohn) localization A→σ⁻¹A which is injective and stably flat we obtain a lifting theorem for induced f.g. projective σ⁻¹A-module chain complexes and localization exact sequences in algebraic L-theory, matching the algebraic K-theory localization exact sequence of Neeman-Ranicki [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] and Neeman [Amnon Neeman, Noncommutative localisation in algebraic K-theory II, Adv. Math. 213 (2007) 785-819].     

Self-approximation of Dirichlet L-functions

Let d be a real number, let s be in a fixed compact set of the strip 1/2<σ<1, and let L(s,χ) be the Dirichlet L-function. The hypothesis is that for any real number d there exist ‘many’ real numbers τ such that the shifts L(s+iτ,χ) and L(s+idτ,χ) are ‘near’ each other. If d is an algebraic irrational number then this was obtained by T. Nakamura. ?. Pańkowski solved the case then d is a transcendental number. We prove the case then d≠0 is a rational number. If d=0 then by B. Bagchi we know that the above hypothesis is equivalent to the Riemann hypothesis for the given Dirichlet L-function. We also consider a more general version of the above problem.     

Sums of commutators in non-commutative Banach function spaces

Let M be a II_∞-factor and denote by τ its normal faithful semi-finite trace. For any rearrangement invariant Köthe function space X on [0,+∞[, let X(M,τ) be the associated non-commutative Banach function space. This paper is concerned with ideals in M of the form I_X(M,τ)=M∩X(M,τ) that are contained in L^p(M,τ) for some p>0. It is proved that an element T in I_X(M,τ) is a finite sum of commutators of the form [A,B] with A∈I_X(M,τ) and B∈M if and only if the function belongs to X, where ν_T is the Brown spectral measure of T and t→λ_t(T) is the non-increasing rearrangement of the function λ→|λ| with respect to ν_T. This extends to general Banach function spaces a result obtained by Kalton for quasi-Banach ideals of compact operators and implies that the Dixmier's trace of a quasi-nilpotent element in L^1,∞(M,τ) is always zero.     

Approximating term structure of interest rates using cubic L1 splines

Classical spline fitting methods for estimating the term structure of interest rates have been criticized for generating highly fluctuating fitting curves for bond price and discount function. In addition, the performance of these methods usually relies heavily on parameter tuning involving human judgement. To overcome these drawbacks, a recently developed cubic L₁ spline model is proposed for term structure analysis. Cubic L₁ splines preserve the shape of the data, exhibit no extraneous oscillation and have small fitting errors. Cubic L₁ splines are tested using a set of real financial data and compared with the widely used B-splines.     

Basic Fourier series on a q-linear grid: Convergence theorems

For 0<q<1 define the symmetric q-linear operator acting on a suitable function f(x) by δf(x)=f(q1/2x)−f(q−1/2x). The q-linear initial value problem , f(0)=1, has two entire functions Cq(z) and Sq(z) as linearly independent solutions, which are orthogonal on a discrete set. Sufficient conditions for pointwise convergence and for uniform convergence of the corresponding Fourier expansion are given.     

Explicit solution of the finite time L2-norm polynomial approximation problem

The aim of this paper is to present a new approach to the finite time L₂-norm polynomial approximation problem. A new formulation of this problem leads to an equivalent linear system whose solution can be investigated analytically. Such a solution is then specialized for a polynomial expressed in terms of Laguerre and Bernstein basis.     

On L-convergence of trigonometric series

In the present paper we consider the trigonometric series with (β,r)-general monotone and (β,r)-rest bounded variation coefficients. Necessary and sufficient conditions of L-convergence for such series are obtained in terms of the coefficients. Moreover, we generalize and extend the Tikhonov results [J. Math. Anal. Appl. 347 (2008) 416-427] to the class GM(β,r) or the class RBVS(β,r).     

On the behavior of some two-variable p-adic L-functions

We give some p-adic integral representations for the two-variable p-adic L-functions introduced recently by G. Fox. For powers of the Teichmüller character, we use the integral representation to extend the L-function to a larger domain, in which it is a meromorphic function in the first variable and an analytic element in the second. These integral representations imply systems of congruences for the generalized Bernoulli polynomials, improving previous results of Fox, Gunaratne, and the author; they also lead to generalizations of some formulas of Diamond and of Ferrero and Greenberg for p-adic L-functions in terms of the p-adic gamma and log gamma functions.