Irene Sabadini
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Irene Sabadini has a total of 108 co-authors. Here are the top co-authors by number of shared publications:
- Fabrizio Colombo
Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
148 shared publications - Daniel Alpay
Department of Mathematics, Chapman University, Orange, USA
69 shared publications - Daniele C. Struppa
Chapman University
50 shared publications - Kamal Diki
Clifford Research Group, Department of Electronics and Information Systems Faculty of Engineering and Architecture, Ghent University , Krijgslaan 281, 9000 Ghent
20 shared publications - Guangbin Ren
Department of Mathematics, University of Science and Technology of China, Hefei, People’s Republic of China
12 shared publications - José Oscar González-Cervantes
Departamento de Matemáticas, ESFM, Instituto Politécnico Nacional, Ciudad México, Mexico
12 shared publications
Latest Publications
- Open Access
- 11 September 2026
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 59 (36) , 365203
On the approximation of Weierstrass function via superoscillations
Superoscillations have attracted considerable interest among mathematicians, physicists, and signal-processing engineers over several decades, since the seminal works of Aharonov et al (1988 Phys. Rev. Lett. 60 1351–1354) and of Berry (1994 Quantum Coherence and Reality; in celebration of the 60th Birthday of Yakir Aharonov 55–65) on band-limited functions that locally oscillate faster than their highest Fourier frequency. A particularly intriguing question, posed by Berry and Morley-Short (2017 J. Phys. A: Math. Theor. 49 065203), asks whether such sequences, can reproduce fractals, nowhere-differentiable functions. This question represents an extreme application of superoscillations, well beyond the previously studied regimes of physical interest involving variations on fine but finite scales, and is directly motivated by current applications in physics such as superresolution microscopy and the analysis of sub-wavelength optical and quantum fields. The present paper gives a rigorous affirmative answer for the classical Weierstrass function, and clarifies the exact sense in which the approximation holds.
- 11 September 2026
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 59 (36) , 365203
Open AccessOn the approximation of Weierstrass function via superoscillations
Superoscillations have attracted considerable interest among mathematicians, physicists, and signal-processing engineers over several decades, since the seminal works of Aharonov et al (1988 Phys. Rev. Lett. 60 1351–1354) and of Berry (1994 Quantum Coherence and Reality; in celebration of the 60th Birthday of Yakir Aharonov 55–65) on band-limited functions that locally oscillate faster than their highest Fourier frequency. A particularly intriguing question, posed by Berry and Morley-Short (2017 J. Phys. A: Math. Theor. 49 065203), asks whether such sequences, can reproduce fractals, nowhere-differentiable functions. This question represents an extreme application of superoscillations, well beyond the previously studied regimes of physical interest involving variations on fine but finite scales, and is directly motivated by current applications in physics such as superresolution microscopy and the analysis of sub-wavelength optical and quantum fields. The present paper gives a rigorous affirmative answer for the classical Weierstrass function, and clarifies the exact sense in which the approximation holds.
- 11 August 2026
- Published by Springer Nature
- p. 1983-2011
Hermitian Clifford Analysis
- 11 August 2026
- Published by Springer Nature
- p. 2115-2158
Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case
- 11 August 2026
- Published by Springer Nature
- p. 2115-2158
Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case
- 11 August 2026
- Published by Springer Nature
- p. 2881-2909
Superoscillating Sequences in Several Variables
- 11 August 2026
- Published by Springer Nature
- p. 2881-2909
Superoscillating Sequences in Several Variables
- 11 August 2026
- Published by Springer Nature
- p. 2809-2834
Introduction to Superoscillations: Past and Present
- 11 August 2026
- Published by Springer Nature
- p. 2809-2834
Introduction to Superoscillations: Past and Present
- 11 August 2026
- Published by Springer Nature
- p. 2159-2204
Slice Hyperholomorphic Functional Calculi and the Spectral Theorem on the S-Spectrum
- 11 August 2026
- Published by Springer Nature
- p. 2159-2204
Slice Hyperholomorphic Functional Calculi and the Spectral Theorem on the S-Spectrum
- Open Access
- 4 August 2026
- Published by Springer Nature in Advances in Applied Clifford Algebras
- Vol. 36 (4) , 39
Convergence Domains of Sedenionic Star-Power Series
The theory of slice regular (also called slice hyperholomorphic) functions is a generalization of complex analysis originally given in the quaternionic framework, and then further extended to Clifford algebras, octonions, and to real alternative algebras. Recently, we have extended this theory to the case of (real) even-dimensional Euclidean space. We provided several tools for studying slice regular functions in this context, such as a path-representation formula, slice-solutions, hyper-solutions and hyper- $$\sigma $$ -balls. When adding an algebra structure to Euclidean space we have more properties related to the possibility of multiplying elements in the algebra. In this paper, we focus on exploring the properties specific to the context of the algebra of sedenions which is rather peculiar, being the algebra non associative and non alternative. The consideration of a non alternative algebra is a novelty in the context of slice regularity which opens the way to a number of further progresses. We offer an explicit characterization for slice-solutions and hyper-solutions, and we determine the convergence domain of the $$*$$ -power series with sedenionic coefficients. Unlike the case of complex numbers and quaternions, the convergence domain in this context is determined by two convergence radii instead of one. This result is a new feature appearing in the algebra of sedenions.- 4 August 2026
- Published by Springer Nature in Advances in Applied Clifford Algebras
- Vol. 36 (4) , 39
Open AccessConvergence Domains of Sedenionic Star-Power Series
The theory of slice regular (also called slice hyperholomorphic) functions is a generalization of complex analysis originally given in the quaternionic framework, and then further extended to Clifford algebras, octonions, and to real alternative algebras. Recently, we have extended this theory to the case of (real) even-dimensional Euclidean space. We provided several tools for studying slice regular functions in this context, such as a path-representation formula, slice-solutions, hyper-solutions and hyper- $$\sigma $$ -balls. When adding an algebra structure to Euclidean space we have more properties related to the possibility of multiplying elements in the algebra. In this paper, we focus on exploring the properties specific to the context of the algebra of sedenions which is rather peculiar, being the algebra non associative and non alternative. The consideration of a non alternative algebra is a novelty in the context of slice regularity which opens the way to a number of further progresses. We offer an explicit characterization for slice-solutions and hyper-solutions, and we determine the convergence domain of the $$*$$ -power series with sedenionic coefficients. Unlike the case of complex numbers and quaternions, the convergence domain in this context is determined by two convergence radii instead of one. This result is a new feature appearing in the algebra of sedenions. - Open Access
- 10 April 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (5) , 177
The S-Resolvent Estimates for the Dirac Operator on Hyperbolic and Spherical Spaces
This seminal paper marks the beginning of our investigation on the spectral theory based on S -spectrum applied to the Dirac operator on manifolds. Specifically, we examine in detail the cases of the Dirac operator $$\mathcal {D}_H$$ on hyperbolic space and of the Dirac operator $$\mathcal {D}_S$$ on the spherical space, where these operators, and their squares $$\mathcal {D}_H^2$$ and $$\mathcal {D}_S^2$$ , can be written in an explicit form. This fact is very important for the applications of the spectral theory on the S -spectrum. In fact, let T denote a (right) linear Clifford operator, the S -spectrum is associated with a second-order polynomial in the operator T , specifically the operator defined as $$Q_s(T) := T^2 - 2s_0T + |s|^2.$$ This allows us to associate to the Dirac operator boundary conditions that can be of Dirichlet type but also of Robin-like type. Moreover, our theory is not limited to Hilbert modules but it is applicable to Banach modules as well. The spectral theory based on the S -spectrum has gained increasing attention in recent years, particularly as it aims to provide quaternionic quantum mechanics with a solid mathematical foundation from the perspective of spectral theory. This theory was extended to Clifford operators, and more recently, the spectral theorem has been adapted to this broader context. Moreover, the S -spectrum is crucial for defining the so-called S -functional calculus for quaternionic and Clifford operators in various forms. This includes bounded as well as unbounded operators, where suitable estimates of sectorial and bi-sectorial type for the S -resolvent operator are essential for the convergence of the Dunford integrals in this setting.- 10 April 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (5) , 177
Open AccessThe S-Resolvent Estimates for the Dirac Operator on Hyperbolic and Spherical Spaces
This seminal paper marks the beginning of our investigation on the spectral theory based on S -spectrum applied to the Dirac operator on manifolds. Specifically, we examine in detail the cases of the Dirac operator $$\mathcal {D}_H$$ on hyperbolic space and of the Dirac operator $$\mathcal {D}_S$$ on the spherical space, where these operators, and their squares $$\mathcal {D}_H^2$$ and $$\mathcal {D}_S^2$$ , can be written in an explicit form. This fact is very important for the applications of the spectral theory on the S -spectrum. In fact, let T denote a (right) linear Clifford operator, the S -spectrum is associated with a second-order polynomial in the operator T , specifically the operator defined as $$Q_s(T) := T^2 - 2s_0T + |s|^2.$$ This allows us to associate to the Dirac operator boundary conditions that can be of Dirichlet type but also of Robin-like type. Moreover, our theory is not limited to Hilbert modules but it is applicable to Banach modules as well. The spectral theory based on the S -spectrum has gained increasing attention in recent years, particularly as it aims to provide quaternionic quantum mechanics with a solid mathematical foundation from the perspective of spectral theory. This theory was extended to Clifford operators, and more recently, the spectral theorem has been adapted to this broader context. Moreover, the S -spectrum is crucial for defining the so-called S -functional calculus for quaternionic and Clifford operators in various forms. This includes bounded as well as unbounded operators, where suitable estimates of sectorial and bi-sectorial type for the S -resolvent operator are essential for the convergence of the Dunford integrals in this setting. - Open Access
- 3 March 2026
- Published by Springer Nature in Complex Analysis and Operator Theory
- Vol. 20 (3) , 69
Some Infinite Order Differential Operators Associated with Superoscillations in Several variables
This paper aims to contribute to the theory of superoscillations and supershifts. It provides an overview and new insights into the theory. A crucial role in the evolution of superoscillations and supershifts is played by infinite-order differential operators acting on a suitable class of holomorphic functions. In this work, we consider partial differential equations with a convolution term and determine the corresponding expressions for their associated infinite-order operators. We also consider linear partial differential-difference equations, defining the associated infinite-order differential operator in this case.
- 3 March 2026
- Published by Springer Nature in Complex Analysis and Operator Theory
- Vol. 20 (3) , 69
Open AccessSome Infinite Order Differential Operators Associated with Superoscillations in Several variables
This paper aims to contribute to the theory of superoscillations and supershifts. It provides an overview and new insights into the theory. A crucial role in the evolution of superoscillations and supershifts is played by infinite-order differential operators acting on a suitable class of holomorphic functions. In this work, we consider partial differential equations with a convolution term and determine the corresponding expressions for their associated infinite-order operators. We also consider linear partial differential-difference equations, defining the associated infinite-order differential operator in this case.
- 20 February 2026
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
Generalized partial-slice monogenic functions: the octonionic case
In a recent paper [Trans. Amer. Math. Soc. 378 (2025), pp. 851–883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The present paper shall extend the study of generalized partial-slice monogenic functions from the associative case of Clifford algebras to non-associative alternative algebras, such as octonions. The new class of functions encompasses the regular functions [Rend. Sem. Mat. Univ. Padova 50 (1973), pp. 251–267] and slice regular functions [Rocky Mountain J. Math. 40 (2010), no. 1, 225–241] over octonions, indeed both appear in the theory as special cases. In the non-associative setting of octonions, we shall develop some fundamental properties such as identity theorem, Representation Formula, Cauchy (and Cauchy-Pompeiu) integral formula, maximum modulus principle, Fueter polynomials, Taylor series expansion. As a complement, the paper also introduces and discusses the notion of generalized partial-slice (and regular) functions. Although the study is limited to the case of octonions, it is clear from the statements and the arguments in the proofs that the results hold more in general in real alternative algebras equipped with a notion of conjugation.
- 20 February 2026
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
Generalized partial-slice monogenic functions: the octonionic case
In a recent paper [Trans. Amer. Math. Soc. 378 (2025), pp. 851–883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The present paper shall extend the study of generalized partial-slice monogenic functions from the associative case of Clifford algebras to non-associative alternative algebras, such as octonions. The new class of functions encompasses the regular functions [Rend. Sem. Mat. Univ. Padova 50 (1973), pp. 251–267] and slice regular functions [Rocky Mountain J. Math. 40 (2010), no. 1, 225–241] over octonions, indeed both appear in the theory as special cases. In the non-associative setting of octonions, we shall develop some fundamental properties such as identity theorem, Representation Formula, Cauchy (and Cauchy-Pompeiu) integral formula, maximum modulus principle, Fueter polynomials, Taylor series expansion. As a complement, the paper also introduces and discusses the notion of generalized partial-slice (and regular) functions. Although the study is limited to the case of octonions, it is clear from the statements and the arguments in the proofs that the results hold more in general in real alternative algebras equipped with a notion of conjugation.