Antonio Di Teodoro

Generalized monogenic functions satisfying differential equations with anti-monogenic right-hand sides on Clifford algebras depending on parameters

The equation Du = F(x, u) in Clifford algebras depending on parameters is considered, where D is the Cauchy–Riemann operator. A sufficient condition for the right-hand side of the equation to be anti-monogenic is given. The given criterion enables the construction of anti-monogenic functions in Clifford algebras depending on parameters and yields interior L p -estimates as well. The results provide generalizations of those in Tutschke and Yuksel (1999) [W. Tutschke and U. Yuksel, Generalized Monogenic Functions Satisfying Differential Equations with Anti-Monogenic Right-Hand Sides, ISAAC Series, Vol. 6, Kluwer Academic Publishers, Dordrecht, 1999, pp. 263–270].The equation Du = F(x, u) in Clifford algebras depending on parameters is considered, where D is the Cauchy–Riemann operator. A sufficient condition for the right-hand side of the equation to be anti-monogenic is given. The given criterion enables the construction of anti-monogenic functions in Clifford algebras depending on parameters and yields interior L p -estimates as well. The results provide generalizations of those in Tutschke and Yüksel (1999) [W. Tutschke and U. Yüksel, Generalized Monogenic Functions Satisfying Differential Equations with Anti-Monogenic Right-Hand Sides, ISAAC Series, Vol. 6, Kluwer Academic Publishers, Dordrecht, 1999, pp. 263–270].

Laser-induced modulation of the Landau level structure in single-layer graphene

We present perturbative analytical results of the Landau level quasienergy spectrum, autocorrelation function, and out-of-plane pseudospin polarization for a single graphene sheet subject to intense circularly polarized Terahertz radiation. For the quasienergy spectrum, we find a striking nontrivial level-dependent dynamically induced gap structure. This photoinduced modulation of the energy band structure gives rise to shifts of the revival times in the autocorrelation function and it also leads to modulation of the oscillations in the dynamical evolution of the out-of-plane pseudospin polarization, which measures the angular momentum transfer between light and graphene electrons. For a coherent state, chosen as an initial pseudospin configuration, the dynamics induces additional quantum revivals of the wave function that manifest as shifts of the maxima and minima of the autocorrelation function, with additional partial revivals and beating patterns. These additional maxima and beating patterns stem from the effective dynamical coupling of the static eigenstates. We discuss the possible experimental detection schemes of our theoretical results and their relevance in new practical implementation of radiation fields in graphene physics.

Cauchy–Pompeiu Formula for Multi-meta-weighted-monogenic Functions of first class

In this paper we give a Cauchy–Pompeiu type integral formula for a class of functions called multi-meta-weighted-monogenic using a distance calculated via the quadratic form associated with an elliptic operator. This is used for the construction of the kernel over the domain \(\mathbb{R}^{m+1}\), constructed by fixing the real part for all products of

Generalized Cauchy-Riemann-type operators and some integral representation formulas

\mathbb{R}^{m+1}=\mathbb{R}^{m_1}\times \mathbb{R}^{m_2}\times \cdots \times \mathbb{R}^{m_n}

Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters

Also, we present a section where we discuss the inhomogeneous meta-n-weighted- monogenic equation and a distributional solution for this equation is obtained. In some special cases, the distributional solution becomes a classical solution.

A Modified Dirac Operator in Parameter–Dependent Clifford Algebra: A Physical Realization

Abstract In this paper we solve a Dirichlet problem in ℝ3 for the equation Dnu = 0, where Dn is the n-th power of generalized Cauchy-Riemann operator and u is a Clifford algebra depending on parameters valued function.

A Cauchy–Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations

We introduce some generalized Cauchy-Riemann-type operators. For some of them we give integral representation formulas which allow to study boundary value problems involving these operators.

Fundamental Solutions for Second Order Elliptic Operators in Clifford-Type Algebras

A metamonogenic of first-order function or simply metamonogenic function is a function that satisfies the differential equation \( (D-\lambda)u=0 \) where D is the Cauchy–Riemann operator and λ can be real or Cliffordvalued constant (see [4]). Using this definition we can say that a multimetamonogenic function u is separately metamonogenic in several variables \( x^{(\mathit j)}, j=1,...{\mathit n} \;\rm {with} \; {\mathit n} \geq 2, \rm {if} \; {\mathit x}^{(\mathit j)}=({\mathit x}_{1}^{(\mathit j)},...,{\mathit x}_{{\mathit m}_{\mathit j}}^{(\mathit j)}) \) runs in the Euclidean space \( \mathbb{R}^{m_j} \ \rm{and} \, ({\mathit D}_{\mathit j}-\lambda){\mathit u} = 0,\rm {for \ each} \ {\mathit j}=1,...,{\mathit n},,\) where D j is the corresponding Cauchy–Riemann operator in the space \( \mathbb{R}^{m_j}. \) Using the theory of algebras of Clifford type depending on parameters (see [11, 12]), the present proposal discusses the properties of u in case the dimensions mj are different from each other for multi Mq-monogenic functions, following the ideas exhibited in [9, 10].