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1.
José Rodríguez 《Czechoslovak Mathematical Journal》2006,56(3):805-825
We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention
on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff
integral was first considered by Dobrakov under the name S*-integral. Our main result states that S*-integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function
is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable). 相似文献
2.
U. Luther 《Annali di Matematica Pura ed Applicata》2003,182(2):161-200
We show that the representation theorem for classical approximation spaces can be generalized to spaces A(X,l
q
(ℬ))={f∈X:{E
n
(f)}∈l
q
(ℬ)} in which the weighted l
q
-space l
q
(ℬ) can be (more or less) arbitrary. We use this theorem to show that generalized approximation spaces can be viewed as real
interpolation spaces (defined with K-functionals or main-part K-functionals) between couples of quasi-normed spaces which satisfy certain Jackson and Bernstein-type inequalities. Especially,
interpolation between an approximation space and the underlying quasi-normed space leads again to an approximation space.
Together with a general reiteration theorem, which we also prove in the present paper, we obtain formulas for interpolation
of two generalized approximation spaces.
Received: December 6, 2001; in final form: April 2, 2002?Published online: March 14, 2003 相似文献
3.
By using p-adic q-deformed fermionic integral on ℤ
p
, we construct new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ. By applying Mellin transformation and derivative operator
to these functions, we define twisted (h, q)-extension of zeta functions and l-functions, which interpolate the twisted (h, q)-extension of Euler numbers at negative integers. Moreover, we construct the partially twisted (h, q)-zeta function. We give some relations between the partially twisted (h, q)-zeta function and twisted (h, q)-extension of Euler numbers.
相似文献
4.
We prove the following theorem. Assume f ∈ L
∞(R
2) with bounded support. If f is continuous at some point (x
1,x
2) ∈ R
2, then the double Fourier integral of f is strongly q-Cesàro summable at (x
1,x
2) to the function value f(x
1,x
2) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset
of R
2, then the strong q-Cesàro summability of the double Fourier integral of f is locally uniform on
.
Research partially supported by the Australian Research Council and the Hungarian National Foundation for Scientific Research
under Grant T 046 192. 相似文献
5.
Hans Schoutens 《Monatshefte für Mathematik》2007,161(1):249-261
Let R be a (mixed characteristic) Artinian local ring of length l and let X be an n-tuple of variables. We prove that several algebraic constructions in the ring R[X] admit uniform bounds on the degrees of their output in terms of l, n and the degrees of the input. For instance, if I is an ideal in R[X] generated by polynomials g
i
of degree at most d and if f is a polynomial of degree at most d belonging to I, then f = q
1
f
1 + ··· + q
s
f
s
, for some q
i
of degree bounded in terms of d, l and n only. Similarly, the module of syzygies of I is generated by tuples all of whose entries have degree bounded in terms of d, l and n only. 相似文献
6.
Tomohito Naito Kohei Asai Tomoyuki Amano Masanobu Taniguchi 《Statistical Inference for Stochastic Processes》2010,13(3):163-174
In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local
Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary
process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density f
θ
(λ) around λ, we propose a local estimator [^(q)] = [^(q)] (l){\hat{\theta } = \hat{\theta } (\lambda ) } of θ which maximizes the local Whittle likelihood around λ, and use f[^(q)] (l) (l){f_{\hat{\theta } (\lambda )} (\lambda )} as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic
based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their
asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary
time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated
by a few simulated numerical examples. 相似文献
7.
Hans Schoutens 《Monatshefte für Mathematik》2007,150(3):249-261
Let R be a (mixed characteristic) Artinian local ring of length l and let X be an n-tuple of variables. We prove that several algebraic constructions in the ring R[X] admit uniform bounds on the degrees of their output in terms of l, n and the degrees of the input. For instance, if I is an ideal in R[X] generated by polynomials g
i
of degree at most d and if f is a polynomial of degree at most d belonging to I, then f = q
1
f
1 + ··· + q
s
f
s
, for some q
i
of degree bounded in terms of d, l and n only. Similarly, the module of syzygies of I is generated by tuples all of whose entries have degree bounded in terms of d, l and n only. 相似文献
8.
《Quaestiones Mathematicae》2013,36(4):451-466
Abstract Let d be a positive integer, and F be a field of characteristic zero. Suppose that for each positive integer n, I n, is a GL n,(F)- invariant of forms of degree d in x1, …, x n, over F. We call {I n} an additive family of invariants if I p+q (f ⊥ g) = I p(f).I q(g) whenever f; g are forms of degree d over F in x l, …, x p; …, x q respectively, and where (f ⊥ g)(x l, …, x p+q) = f(x 1, …, x p,) + g (x p+1, …, x p+q). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the symbolic method for representing invariants of a form, which we review. 相似文献
9.
The rate of convergence of q-Bernstein polynomials for 总被引:3,自引:0,他引:3
In the note, we obtain the estimates for the rate of convergence for a sequence of q-Bernstein polynomials {Bn,q(f)} for 0<q<1 by the modulus of continuity of f, and the estimates are sharp with respect to the order for Lipschitz continuous functions. We also get the exact orders of convergence for a family of functions , and the orders do not depend on α, unlike the classical case. 相似文献
10.
Let E be a Banach lattice and L1(μ, E) be the space of E-valued Bochner integrable functions. Some order properties of L1(μ, E) are given. It is shown that Ls∞(μ, Z(E)) is the ideal centre of L1(μ, E) and it is obtained a Radon-Nikodym type theorem for B -integrable functions.
相似文献
11.
In this paper, we discuss properties of the ω,q-Bernstein polynomials introduced by S. Lewanowicz and P. Woźny in [S. Lewanowicz, P. Woźny, Generalized Bernstein polynomials, BIT 44 (1) (2004) 63–78], where fC[0,1], ω,q>0, ω≠1,q−1,…,q−n+1. When ω=0, we recover the q-Bernstein polynomials introduced by [G.M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511–518]; when q=1, we recover the classical Bernstein polynomials. We compute the second moment of , and demonstrate that if f is convex and ω,q(0,1) or (1,∞), then are monotonically decreasing in n for all x[0,1]. We prove that for ω(0,1), qn(0,1], the sequence converges to f uniformly on [0,1] for each fC[0,1] if and only if limn→∞qn=1. For fixed ω,q(0,1), we prove that the sequence converges for each fC[0,1] and obtain the estimates for the rate of convergence of by the modulus of continuity of f, and the estimates are sharp in the sense of order for Lipschitz continuous functions. 相似文献
12.
Vladimir Dobrić 《Journal of Theoretical Probability》1994,7(1):129-134
IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f
1+f
2, wheref
1 is Bochner -integrable andf
2 is Pettis -integrable with Pettis norm 0. The decomposition is unique. 相似文献
13.
Dug Hun Hong 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7296-7303
The classical Liapunov inequality shows an interesting upper bound for the Lebesgue integral of the product of two functions. This paper proposes a Liapunov type inequality for Sugeno integrals. That is, we show that holds for some constant Hs,t,r where 0<t<s<r,f:[0,1]→[0,∞) is a non-increasing concave function, and μ is the Lebesgue measure on R. We also present two interesting classes of functions for which the classical Liapunov type inequality for Sugeno integrals with Hs,t,r=1 holds. Some examples are provided to illustrate the validity of the proposed inequality. 相似文献
14.
In this note,we prove that the Toeplitz-type Operator Θ b α generated by the generalized fractional integral,Calderón-Zygmund operator and VMO funtion is bounded from L p,λ (R n) to L q,μ (R n).We also show that under some conditions Θαb f ∈ V L q,μ (B R),the vanishing-Morrey space. 相似文献
15.
It is shown that if {y
n} is a block of type I of a symmetric basis {x
n} in a Banach spaceX, then {y
n} is equivalent to {x
n} if and only if the closed linear span [y
n] of {y
n} is complemented inX. The result is used to study the symmetric basic sequences of the dual space of a Lorentz sequence spaced(a, p). Let {x
n,f
n} be the unit vector basis ofd(a, p), for 1≤p<+∞. It is shown that every infinite-dimensional subspace ofd(a, p) (respectively, [f
n] has a complemented subspace isomorphic tol
p (respectively,l
q, 1/p+1/q=1 when 1<p<+∞ andc
0 whenp=1) and numerous other results on complemented subspaces ofd(a, p) and [f
n] are obtained. We also obtain necessary and sufficient conditions such that [f
n] have exactly two non-equivalent symmetric basic sequences. Finally, we exhibit a Banach spaceX with symmetric basis {x
n} such that every symmetric block basic sequence of {x
n} spans a complemented subspace inX butX is not isomorphic to eitherc
0 orl
p, 1≤p<+∞. 相似文献
16.
Tord Sj?din 《manuscripta mathematica》2008,127(3):369-380
A theorem of Beurling states that if f satisfies , n = 1, 2,..., for some 0 < ρ < 2, on a real interval I, then f is analytic in a rhombus containing I. We study the corresponding problem for the quantum differences Δ
n
f (q, x), q > 1, n = 1, 2,..., for functions defined on (0, ∞) and prove quantitative and qualitative analogues of Beurling’s result. We also
characterize the analyticity of f on subintervals of (0, ∞) in q-analytic terms. 相似文献
17.
Given a separable Orlicz sequence spacel
F we investigate those Orlicz sequence spacesl
f which are isomorphic to subspaces (respectively complemented subspaces) ofl
F. We give in particular an example of a reflexive Orlicz sequence space which does not contain anyl
p, 1<p<∞, as a complemented subspace. 相似文献
18.
Suppose 1≤p,q≤∞ and α > (1/p−1/q)+. Then we investigate compactness properties of the integral operator when regarded as operator from Lp[0,1] into Lq[0,1]. We prove that its Kolmogorov numbers tend to zero faster than exp(−cαn1/2). This extends former results of Laptev in the case p=q=2 and of the authors for p=2 and q=∞. As application we investigate compactness properties of related integral operators as, for example, of the difference
between the fractional integration operators of Riemann–Liouville and Weyl type. It is shown that both types of fractional
integration operators possess the same degree of compactness. In some cases this allows to determine the strong asymptotic
behavior of the Kolmogorov numbers of Riemann–Liouville operators.
In memoria of Eduard (University of the West Indies) who passed away in October 2004. 相似文献
19.
Fernando Cobos 《Mathematische Nachrichten》1985,120(1):203-216
This paper deals with a new class of perfect Frèchet spaces which can be obtained by interpolation of echelon spaces: lp,q[am,n]. We determine the reflexive, Montel, Schwartz, totally reflexive, totally Montel and nuclear spaces lp,q[am,n]. We also derive results on closed subspaces on the spaces (lp,q)(N). 相似文献
20.
Sofiya Ostrovska 《Archiv der Mathematik》2006,86(3):282-288
Let Bn (f, q; x), n=1, 2, ... , 0 < q < ∞, be the q-Bernstein polynomials of a function f, Bn (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {Bn (f, qn; x)} with qn ↓ 1 is not an approximating sequence for f ∈C[0, 1], in contrast to the standard case qn ↓ 1. At the same time, there exists a sequence 0 < δn ↓ 0 such that the condition
implies the approximation of f by {Bn (f, qn; x)} for all f ∈C[0, 1].
Received: 15 March 2005 相似文献