Analysis Mathematica最新文献

The boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces (A^p_omega(mathbb{B}_n)) induced by a doubling weight (omega) to Lebesgue spaces (L^q_mu(mathbb{B}_n)) are characterized on the unit ball and for the entire range (0<p,q<infty), which extend many results in the literatures. As a byproduct, a new characterization of (q)-Carleson the measure for (A^p_omega(mathbb{B}_n)) in terms of the Bergman metric ball is also presented.

Given separable Hilbert spaces (mathcal{H}), (mathcal{K}_1), and (mathcal{K}_2), we analyze Hilbert-Schmidt frames for (mathcal{H}) with respect to the tensor product (mathcal{K}_1 otimes mathcal{K}_2). First, we give a characterization of Hilbert-Schmidt frames for (mathcal{H}) with respect to ({mathcal{K}_1 otimes mathcal{K}_2}). The construction of the Hilbert-Schmidt frames for (mathcal{H}) with respect to (mathcal{K}_1 otimes mathcal{K}_2) in terms of discrete frames for (mathcal{H}) is presented. Sufficient conditions for the existence of Hilbert-Schmidt dual frames are given. We give the construction of Hilbert-Schmidt orthonormal bases, and sufficient conditions for the existence of Riesz bases for (mathcal{H}) with respect to (mathcal{K}_1 otimes mathcal{K}_2).

In this paper, we consider the equation

where (alpha(x)) is a nonzero rational, (H(x,y)) and (G(x,y)) are co-prime polynomials of (y) with rational coefficients. If there exists a non-rational meromorphic solution with (rho_{2}(y)<1 ), then (deg_{y}(H)) and (deg_{y}(G)) must satisfy certain conditions.

In this paper, we obtain joint simultaneous approximation of analytic functions defined on the strip ({sin mathbb{C}: 1/2< operatorname{Re} s<1}) by shifts ( { (L(s+itau, chi_1), dots, L(s+itau, chi_r)) } ) of Dirichlet (L)-functions with non-equivalent Dirichlet characters in short intervals, i.e., intervals ([T,T+H]) with (T^{27/82} leq H leq T^{1/2}). It is proved that the set of such approximating shifts has a positive lower density, and even positive density for all but at most countably many approximation accuracies. For the proof, the probabilistic approach is used.

We study the complex singularity exponents on the level sets ofthe plurisubharmonic functions. We prove the strong openness conjecture on thelevel sets of plurisubharmonic functions.

The optimal transport and Wasserstein barycenter of Gaussian distributions have been solved. In literature, the closed form formulas of the Monge map, the Wasserstein distance and the Wasserstein barycenter have been given. Moreover, when Gaussian distributions extend more generally to elliptically contoured distributions, similar results also hold true. In this case, Gaussian distributions are regarded as elliptically contoured distribution with generator function (e^{-x/2}). However, there are few results about optimal transport for elliptically contoured distributions with different generator functions. In this paper, we degenerate elliptically contoured distributions to radially contoured distributions and study their optimal transport and prove their Wasserstein barycenter is still radially contoured. For general elliptically contoured distributions, we give two numerical counterexamples to show that the Wasserstein barycenter of elliptically contoured distributions does not have to be elliptically contoured.

In this paper, we define the grand mixed Morrey generalized spaces (mathcal{M}^{P),Psi (.)}_{u}(mathbb{R}^{n})) over Euclidean spaces, where (P=(p_{1} ,ldots,p_{n})), (Psi (.)=(psi_{1} (.) ,ldots,psi_{n} (.))) is an (n)-tuple of positive increasing functions (psi_{i}) defined on ((0,p_{i}-1]) with (p_{i}in(1,infty)) and (i= 1 ,ldots,n), and (u(cdot,cdot)) is a positive Lebesgue measurable function defined on (mathbb{R}^{n}times(0,infty)). We establish embedding and density properties for spaces (mathcal{M}^{P),Psi (.),Sigma}_{u}(mathbb{R}^{n})) with (0<Sigma<P-1). As applications, we prove that the bilinear (omega)-type Calderón-Zygmund operator (widetilde{T}_{omega}) and its commutator (widetilde{T}_{omega,b_{1},b_{2}}) which is formed by (b_{1}, b_{2}inmathrm{BMO}(mathbb{R}^{n})) and (widetilde{T}_{omega}) are bounded from the product of grand mixed generalized Morrey spaces (mathcal{M}^{P_{1}),Theta,Sigma_{1}}_{u_{1}}(mathbb{R}^{n})times mathcal{M}^{P_{2}),Theta,Sigma_{2}}_{u_{2}}(mathbb{R}^{n})) into the spaces (mathcal{M}^{P),Theta,Sigma}_{u}(mathbb{R}^{n})), and they are also bounded from the product of grand mixed Morrey spaces (M^{P_{1}),Theta,Sigma_{1}}_{q_{1}}( mathbb{R}^{n})times M^{P_{2}),Theta,Sigma_{2}}_{q_{2}}(mathbb{R}^{n})) into the spaces (M^{P),Theta,Sigma}_{q}(mathbb{R}^{n})), where (u_{1}u_{2}=u), (Theta=(theta_{1} ,ldots,theta_{n})>0), (frac{1}{P}= frac{1}{P_{1}} +frac{1}{P_{2}}) for (1<P_{1}, P_{2}<infty), (0<Sigma_{i}=(sigma_{i1},sigma_{i2} ,ldots,sigma_{in})<P_{i}-1) ((i=1,2)) and (frac{1}{q}=frac{1}{q_{1}}+frac{1}{q_{2}}) for (1< q_{1}, q_{2}<infty).

This article is focused on exploring finite order transcendentalentire solutions of some non-linear homogeneous differential equations involving(qmbox{-}c)-shift. Our findings are improvements and extensions of some existing resultsin this area, supported by examples. In the last section we are concerned withthe solutions of the (qmbox{-}c)-shift difference equation. We have elucidated that ourgeneralized structured (qmbox{-}c)-shift difference equations allow the existence of higherorder solutions which provides the practical implications of the structure and thussignificantly extend some earlier results in the literature.

Let f be an entire almost periodic function with zeros in a horizontal strip of finite width; for example, any exponential polynomial with purely imaginary exponents is such a function. Let (mu) be the measure on the set of zeros of f whose masses coincide with multiplicities of zeros. We define the Fourier transform in the sense of distributions for (mu) and prove that it is a pure point measure on (mathbb{R}) whose complex masses correspond to coefficients of Dirichlet series of the logarithmic derivative of f . Bases on this description and Meyer’s theorem on quasicrystals, we give a simple necessary and sufficient condition for f to be a finite product of sines.

We prove the lineability of the set of Riemann integrable functions which are not measurable for certain Banach spaces. We also prove that, for a non-Schur space, the set of scalarly Riemann integrable functions which are not Darboux integrable is lineable.