𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Differentiable functions of quaternion variables

✍ Scribed by S.V. Lüdkovsky; F. van Oystaeyen

Publisher
Elsevier Science
Year
2003
Tongue
French
Weight
391 KB
Volume
127
Category
Article
ISSN
0007-4497

No coin nor oath required. For personal study only.

✦ Synopsis

We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass' theorem.

📜 SIMILAR VOLUMES

A differential criterium for regularity
A differential criterium for regularity of quaternionic functions
✍ Alessandro Perotti 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 87 KB

Let Ω ⊆ C 2 . We prove that there exist differential operators T and N, with complex coefficients, such that a function f : Ω → H of class C 1 is regular if and only if (N -jT )f = 0 on ∂Ω (j a basic quaternion) and f is harmonic on Ω. At the same time we generalize a result of Kytmanov and Aizenber

Non-commutative linear algebra and pluri
Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables
✍ Semyon Alesker 📂 Article 📅 2003 🏛 Elsevier Science 🌐 French ⚖ 255 KB

We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables.

Construction of differentiable membershi
Construction of differentiable membership functions
✍ A. Grauel; L.A. Ludwig 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 405 KB

In many applications of fuzzy logic it is of special interest to have a transfer function with good properties regarding differentiability. To that end it is desirable to have continuously differentiable membership functions with only few parameters. In this paper we propose a class of symmetrical a

Online computations of differentiable fu
Online computations of differentiable functions
✍ Matthias Schröder 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 854 KB

We show that Lipschitz-continuously differentiable functions f : ([-I; I])k + R which are computable in time I'( T(n)), where T is regular, can be computed online in time C'( T(n) + .&(n) log(n)) on a Type-2-machine, where .I:n~n log(n) log log(n) is the Schiinhage-Strassenbound for integer multipli