We consider solutions to Schrödinger equation with variable coefficients. Let H be a Schrödinger operator and let u(t) = e−itHu0 with u0 ∈ L(R). We show that the wave front set of u0 in the nontrapping region corresponds to the wave front set of e0u(t), where H0 is the free Schrödinger operator. The correspondence is given by the wave operator for the classical mechanical scattering.

We discuss locality in the domain-wall QCD through the effective four-dimensional Dirac operator which is defined by the transfer matrix of the five-dimensional Wilson fermion. We first derive an integral representation for the effective operator, using the inverse five-dimensional Wilson-Dirac operator with the anti-periodic boundary condition in the fifth direction. Exponential bounds are obt...

We introduce a class of scattering passive linear systems motivated by examples from mathematical physics. The state space of the system is X = H ⊕ E, where H and E are Hilbert spaces. We also have a Hilbert space E0 which is dense in E, with continuous embedding, and E ′ 0 is the dual of E0 with respect to the pivot space E. The input space is the same as the output space, and it is denoted by...

We investigate some extremal cases of exactness constant and completely bounded projection constant. More precisely, for an n-dimensional operator space E we prove that λcb(E) = √ n if and only if ex(E) = √ n, which is equivalent to λcb(E) < √ n if and only if ex(E) < √ n.

Let E be a vector valued sequence space with operator valued βdual E . If E satisfies certain gliding hump assumptions, we show that pointwise bounded subsets of E are sequentially equicontinuous. The result is established by considering uniform convergence of the elements in E .

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

and Applied Analysis 3 Define the operator A : P → E by

This article is one of squeal papers. For this decade, I have been studying the Dirac operator on a submanifold as a restriction of the Dirac operator in E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and complet...

Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication to vector model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that product $A_\Phi A_\Psi$ itself operator.

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in n-dimensional euclidean space E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a con...