10 papers
Spectral projectors of bisectorial Clifford operators and applications to the generalized gradient
Francesco Mantovani, Peter Schlosser
We consider right-linear operators on a right Hilbert module over the Clifford algebra R_n, whose S-spectrum lies in an acute double sector. For these bisectorial operators…
Approximation of Fractals via Lagrange-type Superoscillations
Francesco Mantovani, Daniele C. Struppa
We study the approximation of the Weierstrass function by means of superoscillating sequences. Superoscillatory functions are band-limited functions whose local oscillation rate ca…
Nonlocal Fourier Laws for Heat Propagation via Fractional powers of Vector Operators
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
The present work is devoted to the study of fractional powers of vector operators, with particular emphasis on the gradient operator with non-constant coefficients. Within the sett…
Slice hyperholomorphicity of the -resolvent operators and boundary conditions
Francesco Mantovani
The foundation of spectral theory on the -spectrum can be traced back to the quaternionic framework of quantum mechanics. The concept of -spectrum for quaternionic operators…
The S-functional calculus for the Clifford adjoint operator
F. Colombo, F. Mantovani, P. Schlosser
In this paper, we work within the framework of modules over the Clifford algebra . Our investigation focuses on the S-spectrum and the S-functional calculus in its va…
Quadratic estimates for the -functional calculus of bisectorial Clifford operators
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
The -functional calculus is a two-step procedure, introduced by A. McIntosh, that allows the definition of functions of sectorial operators in Banach spaces. It plays a c…
The -functional calculus for right slice hyperholomorphic functions and right linear Clifford operators
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
In 2016, the spectral theory on the -spectrum was used to establish the -functional calculus for quaternionic or Clifford operators. This calculus applies for example…
Superoscillations in the hypercomplex setting
F. Colombo, F. Mantovani, S. Pinton +1
Superoscillatory functions represent a counterintuitive phenomenon in physics but also in mathematics, where a band-limited function oscillates faster than its highest Fourier comp…
The -functional calculus for bisectorial Clifford operators
Francesco Mantovani, Peter Schlosser
The aim of this article is to introduce the H-infinity functional calculus for unbounded bisectorial operators in a Clifford module over the algebra R_n. While recent studies have…
Spectral properties of the gradient operator with nonconstant coefficients
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
In mathematical physics, the gradient operator with nonconstant coefficients encompasses various models, including Fourier's law for heat propagation and Fick's first law, that rel…