Microlocal Analysis of Generalized Pullbacks of Colombeau Functions
نویسندگان
چکیده
منابع مشابه
Microlocal Analysis of generalized pullbacks of Colombeau functions
In distribution theory the pullback of a general distribution by a C∞function is well-defined whenever the normal bundle of the C∞-function does not intersect the wavefront set of the distribution. However, the Colombeau theory of generalized functions allows for a pullback by an arbitrary c-bounded generalized function. It has been shown in previous work that in the case of multiplication of C...
متن کاملGeophysical modeling and microlocal properties of Colombeau functions
In global seismology Earth’s properties of fractal nature occur. Zygmund classes appear as the most appropriate and systematic way to measure this local fractality. For the purpose of seismic wave propagation, we model the Earth’s properties as Colombeau generalized functions. In one spatial dimension, we have a precise characterization of Zygmund regularity in Colombeau algebras. This is made ...
متن کاملGroup invariant Colombeau generalized functions
We give characterizations for generalized functions invariant under certain group actions, such as groups of rotations and the Lorentz group. In the case of rotations, it answers an open question by M. Oberguggenberger in [3]. Also general one-parameter groups are considered.
متن کاملGeophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity
In global seismology Earth’s properties of fractal nature occur. Zygmund classes appear as the most appropriate and systematic way to measure this local fractality. For the purpose of seismic wave propagation, we model the Earth’s properties as Colombeau generalized functions. In one spatial dimension, we have a precise characterization of Zygmund regularity in Colombeau algebras. This is made ...
متن کاملMicrolocal Asymptotic Analysis in Algebras of Generalized Functions
We introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties of their elements with respect to a regularizing parameter. Contrary to the more classical frequential analysis based on the Fourier transform, we can describe a singular asymptotic spectrum which has good properties w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2008
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-008-9266-7