Group invariant Colombeau generalized functions
نویسندگان
چکیده
منابع مشابه
Group 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 کاملSome Classes of Positive Definite Colombeau Generalized Functions
Positivity and positive definiteness in algebra of generalized functions are studied. Basic definitions and notions of Colombeau algebra of generalized functions are given and some special classes of positive definite generalized functions on those algebras are introduced. Their relation to distributions is also investigated. AMS Mathematics Subject Classification (2000):
متن کاملA concise introduction to Colombeau generalized functions and their applications
A straightforward introduction to the theory of Colombeau generalized functions is given with an emphasis on the underlying concepts in view of their applications to applied and theoretical problems by physicists who do not need to know all the mathematical intricacies of that theory. As an application the meaning of the square of the delta function is discussed in some detail.
متن کاملMicrolocal 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 کاملA New Approach to Temperate Generalized Colombeau Functions
A new approach to the algebra Gτ of temperate nonlinear generalized functions is proposed, in which Gτ is based on the space OM endowed with is natural topology in contrary to previous constructions. Thus, this construction fits perfectly in the general scheme of construction of Colombeau type algebras and reveals better properties of Gτ . This is illustrated by the natural introduction of a re...
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: Monatshefte für Mathematik
سال: 2007
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-007-0485-1