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M. A. Muschietti

Publications and source records attributed to M. A. Muschietti.

6 recordsLinked to original sources
arXiv2004

On the resolvent and spectral functions of a second order differential operator with a regular singularity

We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers of $λ$ which depend on the singularity. The consequences for the pole structure of the $ζ$-function, and the small-$t$ asymptotic expansion of the heat-kernel, are also discussed.

math-ph↗
arXiv2003

Unusual poles of the $ζ$-functions for some regular singular differential operators

We consider the resolvent of a system of first order differential operators with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents powers of $λ$ which depend on the singularity, and can take even irrational values. The consequences for the pole structure of the corresponding $ζ$ and $η$-functions are also discussed.

math-ph↗
arXiv1996

Determinants of Dirac operators with local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.

hep-th↗
arXiv1994

Determinants of elliptic boundary problems for Dirac operators I. Local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary and discuss the ellipticity of boundary problems by using the Calderón projector. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.

funct-an↗
arXiv1993

A calculation with a bi-orthogonal wavelet transformation

We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial eigenfunctions of the Hamiltonian of relativistic Hydrogen-like atoms.

funct-an↗