Advances in Hypercomplex Analysis by Cinzia Bisi, Caterina Stoppato (auth.), Graziano Gentili,

By Cinzia Bisi, Caterina Stoppato (auth.), Graziano Gentili, Irene Sabadini, Michael Shapiro, Franciscus Sommen, Daniele C. Struppa (eds.)

This quantity is meant to gather vital examine effects to the lectures and discussions which came about in Rome, on the INdAM Workshop on varied Notions of Regularity for capabilities of Quaternionic Variables in September 2010. This quantity will acquire contemporary and new effects, that are hooked up to the subject lined through the workshop. The paintings goals at bringing jointly overseas best experts within the box of Quaternionic and Clifford research, in addition to younger researchers attracted to the topic, with the belief of offering and discussing fresh effects, reading new developments and methods within the quarter and, often, of selling medical collaboration. specific awareness is paid to the presentation of other notions of regularity for capabilities of hypercomplex variables, and to the examine of the most positive factors of the theories that they originate.

Show description

Read Online or Download Advances in Hypercomplex Analysis PDF

Similar analysis books

Data Analysis in Forensic Science: A Bayesian Decision Perspective (Statistics in Practice)

This can be the 1st textual content to check using statistical equipment in forensic technological know-how and bayesian facts together. The booklet is divided into components: half One concentrates at the philosophies of statistical inference. bankruptcy One examines the variations among the frequentist, the chance and the Bayesian views, earlier than bankruptcy explores the Bayesian decision-theoretic viewpoint additional, and appears on the advantages it incorporates.

New Developments in Classification and Data Analysis: Proceedings of the Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, University of Bologna, September 22–24, 2003

This quantity comprises revised models of chosen papers offered throughout the biannual assembly of the type and knowledge research team of SocietA Italiana di Statistica, which was once held in Bologna, September 22-24, 2003. The clinical software of the convention incorporated eighty contributed papers. additionally it used to be attainable to recruit six across the world well known invited spe- ers for plenary talks on their present examine works concerning the middle themes of IFCS (the foreign Federation of type Societies) and Wo- gang Gaul and the colleagues of the GfKl prepared a consultation.

Additional info for Advances in Hypercomplex Analysis

Example text

Indeed, the purpose of this paper is to prove an analog of the Bloch-Landau Theorem for slice regular functions. In the complex case, this result is an important fact in the study of the range of holomorphic functions defined on the open unit disc D.

Proof It follows by standard arguments as in the complex case. Remark 4 Let Ω be a given bounded axially symmetric s-domain in H. • Theorem 3 implies that the Bergman spaces A (Ωi ), for i ∈ S2 , are quaternionic right linear Hilbert spaces. • Since f|Ωi = F + Gj where F, G : Ωi → C(i) are holomorphic functions and j ⊥ i, then for f|Ωi ∈ A (Ωi ) there holds: F, G ∈ A (Ωi ). This follows from the inequalities ⎫ ⎪ |F |2 dσi ⎪ ⎬ Ωi ≤ f|Ωi 2A (Ωi ) . ⎪ 2 ⎪ |G| dσi ⎭ Ωi Proposition 1 and Remark 4 imply that given any q ∈ Ωi the evaluation functional φq : A (Ωi ) → H, given by φq [f ] := f (q), ∀f ∈ A (Ωi ), is a bounded quaternionic right-linear functional on A (Ωi ) for every i ∈ S2 .

By a straightforward calculation, similar to the one in the proof of Proposition 2, the following fundamental property is proven. Proposition 7 For α, β ∈ C such that α, β and α + β are different from − m2 − n, n = 0, 1, 2, . . one has (−Δm )α δ ∗ (−Δm )β δ = (−Δm )α+β δ m+4 Corollary 3 For β ∈ C\{± m2 , ± m+2 2 , ± 2 , . } one has (−Δm )β δ ∗ (−Δm )−β δ = δ m+4 Now putting for β ∈ C\{ m2 , m+2 2 , 2 , . } Kβ = (−Δm )−β δ = 2−β Γ ( m−2β 2 ) π m+2β 2 ∗ T−m+2β Boundary Values of Harmonic Potentials in Half-Space 33 and in particular for integer k ⎧ 1 Γ ( m−2k ⎪ −k 2 ) ∗ ⎪ = (−Δ ) δ = T−m+2k , 2k < m when m is even K ⎪ k m ⎪ m+2k 2k ⎪ 2 ⎨ π 2 ) ∗ 1 Γ ( m−2k−1 −k− 12 2 ⎪ ⎪ K δ = T−m+2k+1 , 1 = (−Δm ) ⎪ m+2k+1 k+ 2 2k+1 ⎪ 2 ⎪ π 2 ⎩ 2k < m − 1 when m is odd the above Corollary 3 implies that (−Δm )β [Kβ ] = δ, β ∈ C\ ± (9) m m+2 m+4 ,± ,± ,...

Download PDF sample

Rated 4.56 of 5 – based on 22 votes