Generalized Gaussian measure and a “functional equation”: I
✍ Scribed by Lawrence Corwin
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 841 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0022-1236
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📜 SIMILAR VOLUMES
The paper deals with the functional equation under some special assumptions concerning the given functions u, v and F . Our main result extends some results in the literature.
The stability of the functional equation F (x + y) -G(xy) = 2H (x)K(y) over the domain of an abelian group G and the range of the complex field is investigated. Several related results extending a number of previously known ones, such as the ones dealing with the sine functional equation, the d'Alem
Let g be a smooth function on R n with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that ,(8 &1 (Eg))&E,(8 &1 ( g)) E |{g|. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.
## Abstract We consider the evolution of microstructure under the dynamics of the generalized Benjamin–Bona–Mahony equation equation image with __u__: ℝ^2^ → ℝ. If we model the initial microstructure by a sequence of spatially faster and faster oscillating classical initial data __v^n^__, we obta