Analysis Mathematica最新文献

Generalizing the bounded kernel results of Borgs, Chayes, Lovász, Sós and Vesztergombi [2], we prove two Sampling Lemmas for unbounded kernels with respect to the cut norm. On the one hand, we show that given a (symmetric) kernel (Uin L^p([0,1]^2)) for some (3<p<infty), the cut norm of a random (k)-sample of (U) is with high probability within (O(k^{-frac14+frac{1}{4p}})) of the cut norm of (U). The cut norm of the sample has a strong bias to being larger than the original, allowing us to actually obtain a stronger high probability bound of order (O(k^{-frac 12+frac1p+varepsilon})) for how much smaller it can be (for any (p>2) here). These results are then partially extended to the case of vector valued kernels.

On the other hand, we show that with high probability, the (k)-samples are also close to (U) in the cut metric, albeit with a weaker bound of order (O((ln k)^{-frac12+frac1{2p}})) (for any appropriate (p>2)). As a corollary, we obtain that whenever (Uin L^p) with (p>4), the (k)-samples converge almost surely to (U) in the cut metric as (ktoinfty).

Our goal is to establish Abelian theorems for a variant of theindex Whittaker transform over distributions of compact support.

We investigate the sparse bound for maximal oscillatory singular integrals given by

where (P(x,y)) is a real-valued polynomial on (mathbb{R}^ntimes mathbb{R}^n) and (K) is a Calderón–Zygmund non-convolutional type kernel. We show that (T_{P,K}^*) satisfies an ((r,r))-sparse bound for (1<r<2), which implies the weighted (L^p(1<p<infty)) estimate for the operator (T_{P,K}^*).

A set of bounded linear operators from a Banach space to a Banach lattice is collectively (L)-weakly compact whenever union of images of the unit ball is (L)-weakly compact. In the present note the Meyer-Nieberg duality theorem is extended to collectively (L)-weakly compact sets of operators, the relationship between collectively (L)-weakly compact sets and collectively almost limited sets is investigated, and the domination problem for collectively compact and collectively (L)-weakly compact sets is studied.

Let ({varphi_n}^infty_{n=1}) be a real-valued orthonormal system in (L^2[0,1]), (0<alphaleq 1), (0<varepsilon<alpha), and let ({c_n(f)}^infty_{n=1}) be a sequence of Fourier coefficients of (fin L^2[0,1]) with respect to ({varphi_n}^infty_{n=1}). We prove a sufficient condition on ({varphi_n}^infty_{n=1}) such that the series (sum^infty_{k=1}k^{2(alpha-varepsilon)}c^2_k(f)) converges for any (fin Lip (alpha)). We check that the trigonometric system and the Haar system satisfy this condition. On the other hand, the condition is not fulfilled in general.

In this paper, we investigate a uniqueness question of transcendentalmeromorphic functions sharing three distinct polynomials with theirkth order derivatives, and investigate a uniqueness question of transcendentalmeromorphic functions sharing three distinct small functions with their (k)th orderderivatives, where two of the three distinct small functions are two distinctfinite values. The main results obtained in this paper improve the correspondingresults from Mues–Steinmetz [5], Gundersen [4] and Frank–Schwick [6].

We study a certain family of discrete measures with unit masseson a horizontal strip as an analogue of Fourier quasicrystals on the real line. Weprove a one-to-one correspondence between supports of measures from this familyand zero sets of exponential polynomials with imaginary frequencies. This resultis the special case of a general result on measures whose supports correspond tozero sets of absolutely convergent Dirichlet series with bounded spectrum.

The goal of this paper is to introduce tiling Morrey spaces and their weighted counterparts. A condition under which weights ensure the boundedness of important operators is established. Weights similar to the Muckenhoupt class (A_p) within Morrey spaces are dealt with. Additionally, a full characterization of the weights for which two-weight norm inequalities for linear positive operators hold in these spaces is given. Then new class dealt with in this paper contains the one introduced recently by Lerner.

For a Banach space, the notions of essentially left and right generalized Drazin invertible linear relations are introduced and studied. Then, characterizations of these classes by means of their generalized Saphar decompositions, accumulation and interior points of various spectra are given. Furthermore, sufficient conditions under which an essentially left (resp. right) generalized Drazin invertible linear relation be left (resp. right) Weyl generalized Drazin invertible are provided. In particular, we show that an everywhere defined closed linear relation with a nonempty resolvent set which has the SVEP at (0) (resp. its adjoint has the SVEP at (0)) is essentially left (resp. right) generalized Drazin invertible if and only if it is left (resp. right) Weyl generalized Drazin invertible. The corresponding spectra of such classes are also investigated and concrete examples are illustrated.

Let (mathbb{G}) be a locally compact quantum group. We study theexistence of certain (weakly) compact right and left multipliers of the Banach al-gebra (mathfrak{X} ^{*} ), where (mathfrak{X} ) is an introverted subspace of (L^infty(mathbb{G})) with some conditions, andrelate them with some properties of (mathbb{G}) such as compactness and amenability. Forexample, when (mathbb{G}) is co-amenable and (L^1(mathbb{G})) is semisimple we give a characteri-zation for compactness of (mathbb{G}) in terms of the existence of a nonzero compact rightmultiplier on (mathfrak{X} ^{*} ). Using this, for a locally compact group ({mathcal G}) we prove that (mathbb{G}_a) iscompact if and only if there is a nonzero (weakly) compact right multiplier on (mathfrak{X} ^{*} ).Similar assertion holds for (mathbb{G}_s) when ({mathcal G}) is amenable.