Hypercomplex Analysis and Its Applications

This book contains a collection of short papers based on the presentations given at the international conference on Hypercomplex Analysis and its Applications celebrating Paula Cerejeiras' 60th birthday. These papers present the latest results as well as overviews on specific topics in the areas of hypercomplex and harmonic analysis as well as their connections with partial differential equations and spectral theory.

Covers recent developments in the field of hypercomplex and harmonic analysis Includes contributions by leading experts in the field Collects contributions presented at the International Conference on Hypercomplex Analysis and its Applications

Autorentext

Nelson Faustino is a Portuguese-born mathematician. Currently he is an invited assistant professor at University of Aveiro. He has been part of projects funded by the National Science Foundation of Portugal and has been a scholarship holder of the State Science Foundation of São Paulo, Brazil.

Milton Ferreira is adjunct professor at the Polytechnic University of Leiria since 2008. He has more than 40 publications covering different areas of mathematics such as representation theory, quaternionic and Clifford analysis, gyrogroups, and fractional calculus. He made several oral communications at international meetings.

Uwe Kähler is a professor of mathematics at the University of Aveiro. His main research field is hypercomplex and harmonic analysis and their applications. He is author of more than 100 publications and member of the editorial board in several journals. He is currently president of ISAAC and involved in several projects.

Nelson Vieira is an assistant professor of mathematics at the University of Aveiro. He has more than 50 publications in several fields of mathematics including fractional calculus, neural networks, and hypercomplex analysis. He has organized several scientific meetings and participated in several projects both as a member of the research team or principal researcher.

Inhalt

• 1. Peculiar Behaviors of Functions in q-Calculus.- 2. An introduction to the fine structures on the S-spectrum.- 3. Recovering Composition Algebras from 3D Geometric Algebras.- 4. Characteristics of -Hypermonogenic Functions.- 5. Quaternion Hyperbolic Transforms of the Fourier type - An Overview.- 6. Examples for Rebricking.- 7. Discrete Borel-Pompeiu and Cauchy formulae on a rectangular lattice for bounded domains in R2.- 8. Clifford-Valued B-Splines.- 9. On Clifford Geometric Space-Time Algebras and Symmetries.- 10. Octonionic Hilbert spaces and para-linear operators.- 11. The discrete octonionic Stokes' formula revisited.- 12. An estimate for the dimension of the Kernel of a Singular Integral Operator with two Shifts and Conjugation.- 13. A Bernstein-type inequality for the generalized Dunkl translation.- 14. A zeta function for the bicomplex algebra.- 15. On Grade Automorphism in Ternary Clifford Algebras.- 16. Fractional Polyanalyticity.