Related papers: Fundamental solutions of pseudo-differential opera…
We shall study the solvability of pseudodifferential operators which are not of principal type. The operator will have complex principal symbol satisfying condition ($\Psi$) and we shall consider the limits of semibicharacteristics at the…
We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with four variables over rational function fields of characteristic 2. We apply these results to find prescribed quadratic subfields of quaternion…
A new pseudodifferential calculus of Shubin type is introduced. The calculus contains operators depending on a non negative real parameter as well as operators independent of the parameter. Resolvents of Shubin type pseudodifferential…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
We study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce…
Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.
Solving polynomials is a fundamental computational problem in mathematics. In the real setting, we can use Descartes' rule of signs to efficiently isolate the real roots of a square-free real polynomial. In this paper, we translate this…
In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four…
By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on $\R^n$ as an infinite product of zero-order pseudodifferential operators. A similar representation formula is…
We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce…
We construct polynomial solutions of the KZ differential equations over a finite field $F_p$ as analogs of hypergeometric solutions.
We investigate a new representation of general operators by means of sums of shifted Gabor multipliers. These representations arise by studying the matrix of an operator with respect to a Gabor frame. Each shifted Gabor multiplier…
In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many…
We review recent results on the magnetic pseudo-differential calculus both in symbolic and in $C^*$-algebraic form. We also indicate some applications to spectral analysis of pseudo-differential operators with variable magnetic fields.
In this paper, we consider an analogue of Catalan polynomials and give some identities of symmetry for those polynomials by using fermionic $p$-adic integrals on the ring of $p$-adic integers
Pseudoexponential fields are exponential fields similar to complex exponentiation satisfying the Schanuel Property, which is the abstract statement of Schanuel's Conjecture, and an adapted form of existential closure. Here we show that if…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
In this paper we apply Ax-Schanuel's Theorem to the ultraproduct of $p$-adic fields in order to get some results towards algebraic independence of $p$-adic exponentials for almost all primes $p$.