The minimal operator and the maximal of an elliptic pseudo-differential with symbols on $\mathbb {Z}^n\times \mathbb {T}^n$ are proved to coincide domain is given in terms a Sobolev space. Ellipticity Fredholmness be equivalent for operators {Z}^n$. index {Z}^n$ also computed.

in this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

This paper is concerned with an inverse source problem for the stochastic biharmonic wave equation. The driven assumed to be a microlocally isotropic Gaussian random field its covariance operator being classical pseudo-differential operator. well-posedness of direct examined in distribution sense, and regularity solution discussed given rough source. For problem, strength source, involved princ...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

iut + Lu = F (u), (1) where u : IR × IR → I C and L is a linear (pseudo -) differential operator of order m with real valued symbol denoted by l(ξ), and F is a nonlinear, possibly nonlocal operator. We will only consider the case where the linear part of (1) is dispersive, i.e. l(ξ) 6= Cξ. Actually, we will address cases where the linear group e satisfies some “decay” properties, see Section 1....

The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated sym...

We present a Mathai-Quillen interpretation of topological sigma models. The key to the construction is a natural connection in a suitable infinite dimensional vector bundle over the space of maps from a Riemann surface (the world sheet) to an almost complex manifold (the target). We show that the covariant derivative of the section defined by the differential operator that appears in the equati...

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed 'distorted' Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the ...

We study the solutions of equations of type f(D,α)u = v, where f(D,α) is a p-adic pseudo-differential operator. If v is a Bruhat-Schwartz function, then there exists a distribution Eα, a fundamental solution, such that u = Eα ∗ v is a solution. However, it is unknown to which function space Eα ∗ v belongs. In this paper, we show that if f(D,α) is an elliptic operator, then u = Eα ∗ v belongs to...