Two powerful theorems in Clifford analysis
نویسنده
چکیده
Two useful theorems in Euclidean and Hermitean Clifford analysis are discussed: the Fischer decomposition and the Cauchy-Kovalevskaya extension.
منابع مشابه
Nonlinear and Non-stationary Vibration Analysis for Mechanical Fault Detection by Using EMD-FFT Method
The Hilbert-Huang transform (HHT) is a powerful method for nonlinear and non-stationary vibrations analysis. This approach consists of two basic parts of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). To achieve the reliable results, Bedrosian and Nuttall theorems should be satisfied. Otherwise, the phase and amplitude functions are mixed together and consequently, the ...
متن کاملExtending Two Fixpoint Theorems of Langley and Zheng
We extend two theorems on fixpoints of f(z) by Langley and Zheng [1] to the consideration of points where f(z) = Q(z) for some rational function Q such that Q(∞) =∞. In addition, we extend the class of functions f from transcendental entire functions to meromorphic functions with relatively few poles. Mathematics Subject Classification (1991): 30D30, 30D35
متن کاملGeneralized multidimensional Hilbert transforms in Clifford analysis
During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...
متن کاملClifford Wavelets and Clifford-valued MRAs
In this paper using the Clifford algebra over R4 and its matrix representation, we construct Clifford scaling functions and Clifford wavelets. Then we compute related mask functions and filters, which arise in many applications such as quantum mechanics.
متن کاملPseudoholomorphic punctured spheres in R× (S1 × S2): Moduli space parametrizations
This is the second of two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R × (S1 × S2) as defined by a certain natural pair of almost complex structure and symplectic form. The first article in this series described the local structure of the moduli spaces and gave existence theorems. This article describes a stratification of the moduli spaces and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010