相关论文: Remarks on the Cartan Formula and Its Applications

We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…

We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions…

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…

We extend the universal differential calculus on an arbitrary Hopf algebra to a ``universal Cartan calculus''. This is accomplished by introducing inner derivations and Lie derivatives which act on the elements of the universal differential…

Matrix coordinate transformations are defined as substitution operators without requiring an ordering prescription or an inclusion function from the Abelian coordinate transformations. We construct transforming objects mimicking most of the…

In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to…

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients.…

A new notion of Cartan pairs as a substitute of notion of vector fields in noncommutative geometry is proposed. The correspondence between Cartan pairs and differential calculi is established.

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…

In this paper one sided counterparts of compactness extrapolation results of Hyt\"onen and Lappas are provided. As a consequence of those results, compactness results for one sided singular integrals, commutators of one sided fractional…

We present a complete theory, which is a generalization of Bargmann's theory of factors for ray representations. We apply the theory to the generally covariant formulation of the Quantum Mechanics.

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.

We prove a Calder\'on-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators and generalized Radon transforms.

We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.

We give the normal and anti-normal order expressions of the number operator to the power $k$ by using the commutation relation between the annihilation and creation operators. We use those expressions to give general formulae for functions…

This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.

In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.

This paper is a brief overview of some of our recent results in collaboration with other authors. The cocycle invariants of classical knots and knotted surfaces are summarized, and some applications are presented.

Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…