In this paper, we study the existence of weighted pseudo almost automorphic mild solutions of integro-differential equations with fractional order 1 < α < 2, here A is a linear densely defined operator of sectorial type on a complex Banach space X. This paper also deals with existence of weighted pseudo almost automorphic mild solutions of semilinear integro-differential eqautions with A is the...

The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary conditions. If the Robin sector is modified by the addition of a pseudo-differential boundary operator, gauge-invariant boundary conditions are obtained at t...

We present a conjecture that the universal enveloping algebra of differential operators ∂ ∂tk over C coincides with the universal enveloping algebra of the (Borel subalgebra of) Virasoro generators from the Kontsevich model. Thus, we can decompose any (pseudo)differential operator to some combination of the Virasoro operators. We use this decomposition to present the r.h.s. of the Givental form...

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy E. This permits a detailed study of the spectrum in various asymptotic regions of the parameters (E...

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy E. This permits a detailed study of the spectrum in various asymptotic regions of the parameters (E...

We study the Vladimirov–Taibleson operator, a model example of pseudo-differential operator acting on real- or complex-valued functions defined non-Archimedean local field. prove analogs classical inequalities for fractional Laplacian, counterpart Dirichlet problem including property boundary Hölder regularity solutions.

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a 2× 2 matrix of pseudo-differential operators with pseudo-homogeneous kernels. The request of invariance...

We prove a Liouville-type theorem for bounded stable solutions v ∈ C(R) of elliptic equations of the type (−∆)v = f(v) in R, where s ∈ (0, 1) and f is any nonnegative function. The operator (−∆) stands for the fractional Laplacian, a pseudo-differential operator of symbol |ξ|.