Related papers: Eigenvalues of conformally invariant operators on …
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
Survey about extremum of eigenvalues of geometric operators within a conformal class of a compact riemannian manifold.
In this paper, we establish higher order Borel-Pompeiu formulas for conformally invariant fermionic operators in higher spin theory, which is the theory of functions on m-dimensional Euclidean space taking values in arbitrary irreducible…
For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a particular discrete symmetry. Applications to the PT-symmetric…
The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of…
This paper constructs a family of conformally invariant differential operators acting on spinor densities with leading part a power of the Dirac operator. The construction applies for all powers in odd dimensions, and only for finitely many…
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant…
In this paper, an explicit expression is obtained for the conformally invariant higher spin Laplace operator $\mathcal{D}_{\lambda}$, which acts on functions taking values in an arbitrary (finite-dimensional) irreducible representation for…
We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…
In this paper the conformal Dirac operator on the sphere is defined to be operating on the space of square-integrable Clifford algebra-valued functions. The spinorial Laplacian of order d>0 is defined and used to establish Sobolev embedding…
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
The conformal anomaly for spinors and scalars on a N-dimensional hyperbolic space is calculated explicitly, by using zeta-function regularization techniques and the Selberg trace formula. In the case of conformally invariant spinors and…
In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…
In this article we establish optimal estimates for the first eigenvalue of Schr\"odinger operators on the d-dimensional unit sphere. These estimates depend on Lebsgue's norms of the potential, or of its inverse, and are equivalent to…
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of parameters, and the wavelet transform is invertible directly by…
In this paper we show variant of the spectral theorem using an algebraic Jordan-Schwinger map. The advantage of this approach is that we don't have restriction of normality on the class of operators we consider. On the other side, we have…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…