Related papers: On the trace formula for higher-order ODO
The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in…
For precision studies with QCD observables at colliders, higher order perturbative corrections are often mandatory. For exclusive observables, like jet cross sections or differential distributions, these corrections were until recently only…
This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.
In this paper, we consider the trace property of pseudo-differential operators with symbols in $\alpha$-modulation spaces.
The problem of equivalency for linear differential operators of the first order is discussed.
The Laplacian of a general trace polynomial function defined on the special orthogonal group $SO(N)$ is explicitly computed. An invariant flag of spaces generated by trace polynomials is constructed. The matrix of the Laplace-Beltrami…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
We review matrix methods as applied to tracer transport. Because tracer transport is linear, matrix methods are an ideal fit for the problem. A gridded, Eulerian tracer simulation can be approximated as a system of linear ordinary…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain $\Omega\subset\dR^n$ with smooth compact boundary are studied. A Schatten--von Neumann type…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…
We extend the noncommutative residue of M. Wodzicki on compactly supported classical pseudo-differential operators of order $-d$ and generalise A. Connes' trace theorem, which states that the residue can be calculated using a singular trace…
We give a necessary and sufficient condition on a positive compact operator $T$ for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on $T$. This generalizes…
Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…
Informed by recent work on tensor singular value decomposition and circulant algebra matrices, this paper presents a new theoretical bridge that unifies the hypercomplex and tensor-based approaches to singular value decomposition and robust…