Maps preserving a certain product of operators

Let $$\mathcal {A}$$ be a standard operator algebra on a Banach space $$\mathcal {X}$$ with $$ \dim \mathcal {X}\ge 3$$. In this paper, we determine the form of the bijective maps $$\phi :\mathcal {A}\longrightarrow \mathcal {A}$$ satisfying $$\begin{aligned} \phi \left( \frac{1}{2}(AB^2+B^2A)\right) = \frac{1}{2}[\phi (A)\phi (B)^{2}+\phi (B)^{2}\phi (A)], \end{aligned}$$for every $$A,B \in \mathcal {A}$$.     

Characterization of Normal Traces on Von Neumann Algebras by Inequalities for the Modulus

It is proved that if a normal semifinite weight on a von Neumann algebra satisfies the inequality for any selfadjoint operators in , then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality is refined and reinforced.     

Increasing functions and inverse Santaló inequality for unconditional functions

Let be a convex function and be its Legendre tranform. It is proved that if is invariant by changes of signs, then . This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond. The proof involves a general result on increasing functions on together with a functional form of Lozanovskii’s lemma. In the last section, we prove that for some c > 0, one has always . This generalizes a result of B. Klartag and V. Milman.      

Shifted convolution sums related to Hecke–Maass forms

The Ramanujan Journal - Let $$\phi (z)$$ be a primitive Hecke–Maass cusp forms with Laplace eigenvalue $$\tfrac{1}{4}+t^2$$ . Denote by $$L(s, \mathrm{sym}^m\phi )$$ the m-th symmetric power...     

Supnorm of an eigenfunction of finitely many Hecke operators

The Ramanujan Journal - Let $$\phi $$ be a Laplace eigenfunction on a compact hyperbolic surface attached to an order in a quaternion algebra. Assuming that $$\phi $$ is an eigenfunction of Hecke...     

Spectral method for solving nonlinear wave equations

In this paper,we consider the following nonlinear wave equations:(■~2φ)/(■t~2)-(■~2φ)/(■x~2)+μ~2φ+v~2x~2φ+f(|φ|~2)φ=0,(■~2x)/(■t~2-(■~2X)/(■X~2)+α~2x+α~2x+v~2x|φ|~2+g(X)=0with the periodic-initial conditions:φ(x-π,t)=φ(x+π,t),x(x-π,t)=x(x+v,t),φ(x,0)=■_0(x),φ_t(x,0)=■_1(x),X(x,0)=■_0(x),x_t(x,0)=■_1(x),-∞相似文献   

Convergence of Solutions of General Dispersive Equations Along Curve

In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper.     

The Essential Norm of Hankel Operators on the Weighted Bergman Spaces with Exponential Type Weights

Let denote the closed subspace of consisting of analytic functions in the unit disc . For certain class of subharmonic functions and , it is shown that the essential norm of Hankel operator is comparable to the distance norm from H_f to compact Hankel operators.     

The classical solution of a definite integral occurring in the satellite theory in the extended phase space

The definite integral $$\frac{1}{{2\pi }}\int_0^{2\pi } {\cos } [m\phi + nv(E - \phi - e\sin E]d\phi $$ is solved by repeated application of a Bessel function identity. The classical series for the Bessel functions are then used to expand the solution with respect to the eccentricity.     

Entropy solutions of anisotropic elliptic nonlinear obstacle problem with measure data

We prove the existence of an entropy solution for a class of nonlinear anisotropic elliptic unilateral problem associated to the following equation $$\begin{aligned} -\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) -\sum _{i=1}^{N}\partial _{i}\phi _{i}( u)=\mu , \end{aligned}$$where the right hand side $$\mu $$ belongs to $$L^{1}(\Omega )+ W^{-1, \vec {p'}}(\Omega )$$. The operator $$-\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) $$ is a Leray–Lions anisotropic operator and $$\phi _{i} \in C^{0}({\mathbb {R}}, {\mathbb {R}})$$.     

Asymptotic behavior of ground state radial solutions for problems involving the $$\Phi $$ Φ -Laplacian

Positivity - We are concerned with the existence of positive solutions to the following boundary value problem in $$(0,\infty ),$$ $$\begin{aligned} \frac{1}{A}\left( A\phi \left( \left| u^{\prime...     

Universal inequalities for eigenvalues of a system of elliptic equations of the drifting Laplacian

Let \(\Omega \) be a bounded domain in a n-dimensional Euclidean space \(\mathbb {R}^{n}\). We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting Laplacian

$$\begin{aligned} \left\{ \begin{array}{ll} \mathbb {L_{\phi }}\mathbf{{u}} + \alpha (\nabla (\mathrm {div}{} \mathbf{{u}}) - \nabla \phi \mathrm {div}{} \mathbf{{u}})= -\bar{\sigma }\mathbf{{u}}, &{} \hbox {in} \,\Omega ; \\ \mathbf{{u}}|_{\,\partial \Omega }=0. \end{array} \right. \end{aligned}$$

Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived. Finally, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space.

     

On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus

We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ where C(?) ∈ C′(T _m; a) is a nondegenerate symmetric matrix.     

An Integral Jensen Inequality For Convex Multifunctions

We prove the following multivalued version of the Jensen integral inequality. Let X, Y be Banach spaces and D ? X an open and convex set. If F: D ? cl(Y) is a continuous convex function, then for each normalized measure space (Ω, S, μ), and for all μ-integrable functions ? : Ω ? D such that conv?(Ω) ? D, $$\int_{\Omega}(F\ o\ \phi)d\mu \subset F\Bigg(\int_{\Omega}\phi d\mu\Bigg).$$      

Elliptic Systems with a Partially Sublinear Local Term

Let $1 0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results.     

Global well-posedness of the KP-I initial-value problem in the energy space

We prove that the KP-I initial-value problem

The principal eigenvalue of a space–time periodic parabolic operator

This paper deals with the generalized principal eigenvalue of the parabolic operator , where the coefficients are periodic in t and x. We give the definition of this eigenvalue and we prove that it can be approximated by a sequence of principal eigenvalues associated to the same operator in a bounded domain, with periodicity in time and Dirichlet boundary conditions in space. Next, we define a family of periodic principal eigenvalues associated with the operator and use it to give a characterization of the generalized principal eigenvalue. Finally, we study the dependence of all these eigenvalues with respect to the coefficients.      

Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities

In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation $$ \left\{ - \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3, \right. $$ where $1相似文献   

Characterization of order 3 algebraic immersed minimal surfaces of <Emphasis Type="Italic">S</Emphasis><Superscript>3</Superscript>

In this paper we prove that if is a minimal immersion of a compact surface and , for some homogeneous polynomial f of degree 3 on R ⁴, then, M is a torus and is one of the examples given by Lawson (1970, Complete minimal surfaces in S ³. Ann. Math. 92(2), 335–374).      

非退化扩散过程的水平集和极集

设X(t)(t∈R )是一个d维非退化扩散过程．本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数．