Related papers: The index of singular integral operators with disc…
We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the…
We consider an eigenvalue problem for an inverted one dimensional harmonic oscillator. We find a complete description for the eigenproblem in $C^{\infty}(\mathbb R)$. The eigenfunctions are described in terms of the confluent hypergeometric…
A first order trace formula is obtained for a regular differential operator perturbed by a finite signed measure multiplication operator.
Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the…
The objective of this paper to give a formula for unitary operators that corresponds to the Heler-Sj{\"o}strand formula for self-adjoint operators.
In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.
In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.
In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove…
In this paper, we investigate sharp damping estimates for a class of one dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are…
We describe an algorithm for obtaining generators of the unit group of the integral group ring ZG of a finite abelian group G. We used our implementation in Magma of this algorithm to compute the unit groups of ZG for G of order up to 110.…
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
An integer-valued fixed point index for compositions of acyclic multivalued maps is constructed. This integer-valued fixed point index has the properties: additivity, homotoy invariance, normalization, commutativity, multiplicativity. The…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…
Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the…
The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these…