LITTLEWOOD-PALEY THEOREM FOR SCHR DINGER OPERATORS

Let H be a Schrodinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

LIOUVILLE＇S THEOREM FOR LPDO WITH CONSTANT COEFFICIENTS

In this note, the authors consider a class of linear partial differential operators P(Э) with constant coefficients and prove that the operator P(Э) has Liouville property if and only if the polynomial P(iξ) doesn‘t have roots in R^n\{0}.     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHROEDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schroedinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.     

TWO-WEIGHT NORM INEQUALITIES FOR A CLASS OF ROUGH MULTILINEAR OPERATORS

In this paper,we give the (L^p,L^q)-boundedness for a aclass of multilinear operators with two different wieght functions.     

TIME DECAY FOR SCHROEDINGER EQUATION WITH ROUGH POTENTIALS

We obtain certain time decay and regularity estimates for 3D Schroedinger equation with a potential in the Kato class by using Besov spaces associated with Schroedinger operators.     

A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS

In this article the concept of local conjugation of a C1 mapping between two Banach manifolds is introduced. Then a rank theorem for nonlinear semi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis.     

SUB-SIGNATURE OPERATORS, η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES

The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2, 3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.     

SUB-SIGNATURE OPERATORS,η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES

§0. Introduction Let M be an odd dimensional closed oriented manifold. Let ρbe a unitary represen-tation of the fundamental group of M. By using their η-invariant, Atiyah-Patodi-Singer [2,3] introduced an R/Z-valued smooth invariant associated to …     

THE EXTENSION THEOREM OF-LINEAR RANDOM FUNCTIONALS AND ITS APPLICATIONS

The extension theorem for linear random functionals in linear apaces is proved. And the representation theorem for bounded linear random functionals and the continuous linear random functionals are studied     

SZEGō TYPE FACTORIZATION THEOREM FOR NONCOMMUTATIVE HARDY-LORENTZ SPACES

We introduce noncommutative Hardy-Lorentz spaces and give the Szegō and inner-outer type factorizations of these spaces.     

A REPRESENTATION FORMULA RELATED TO SCHROEDINGER OPERATORS

Schroedinger operator is a central subject in the mathematical study of quantum mechanics.Consider the SchrSdinger operator H=-Δ V on R, where Δ=d^2/dx^2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of-Δ. A natural conjecture is that an L^2 function admits a similar expansion in terms of “eigenfunctions“ of H, a perturbation of the Laplacian (see [7], Ch. XI and the notes), under certain condition on V.     

A Hunziker-van Winter-Zhislin theorem for a four-particle lattice Schrödinger operator

We consider a discrete Schrödinger operator for four arbitrary particles with short-range pair potentials. We describe the position and the structure of its essential spectrum and prove the Hunziker-van Winter-Zhislin theorem.     

Littlewood-Paley operators with variable kernels

In this paper we study a certain directional Hilbert transform and the bound-edness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems.     

Strategies in localization proofs for one-dimensional random Schrödinger operators

Recent results on localization, both exponential and dynamical, for various models of one-dimensional, continuum, random Schrödinger operators are reviewed. This includes Anderson models with indefinite single site potentials, the BernoulliAnderson model, the Poisson model, and the random displacement model. Among the tools which are used to analyse these models are generalized spectral averaging techniques and results from inverse spectral and scattering theory. A discussion of open problems is included.     

Kernel estimates for Schrödinger operators

We prove short time estimates for the heat kernel of Schr?dinger operators with unbounded potential in R^N.     

Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).