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On the solvability of the invariant differential operators on the heisenberg group
Author
Source
Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series
Issue
Vol. 18, Issue 4 (31 Dec. 2003), pp.11-16, 6 p.
Publisher
Mutah University Deanship of Academic Research
Publication Date
2003-12-31
Country of Publication
Jordan
No. of Pages
6
Main Subjects
Abstract AR
العالم الرياضي إهرنبيرز كان أول من برهن أن (Rm) = D (Rm) PD لكل معادلة تفاضلية ثابتة على Rm.
في هذا البحث سوف نبرهن أن (Hn) = D (Hn) PD لكل معادلة تفاضلية ثابتة على زمرةهابسنبيرغ Hn، و بالتالي نبرهن على وجود حل أساسي لهذه المعادلات.
طريقتنا تتكون من قسمة التوزيعات على زمرة هابسنبيرغ، التي تعتمد على تحويل متعلق بالجداء نصف المباشر للزمر.
بهذه الطريقة يتم تحويل المشكلة من التحليل التوافقي الغير تبديلي إلى التحليل التوافقي التبديلي.
Abstract EN
L.Ehrenperis[2] was the first to prove that PD¢ (Rm)=D¢ (Rm) for any invariant differential operator P on R.
The main result is to pove that PD¢ (Hn) = D¢ (Hn) for any invariant differential operator on the real heisebberg group Hn.
Hence to prove the existance of their fundamental soluations, by a transformation, which is associated with the semi-direct product of groups, we construct our method for the division of the distribuations on Hn.
This idea consists of transforming our problem of noncommutative harmonic analysis to an equivalent problem of commutative harmonic analysis.
American Psychological Association (APA)
al-Husayn, K.. 2003. On the solvability of the invariant differential operators on the heisenberg group. Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series،Vol. 18, no. 4, pp.11-16.
https://search.emarefa.net/detail/BIM-366840
Modern Language Association (MLA)
al-Husayn, K.. On the solvability of the invariant differential operators on the heisenberg group. Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series Vol. 18, no. 4 (2003), pp.11-16.
https://search.emarefa.net/detail/BIM-366840
American Medical Association (AMA)
al-Husayn, K.. On the solvability of the invariant differential operators on the heisenberg group. Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series. 2003. Vol. 18, no. 4, pp.11-16.
https://search.emarefa.net/detail/BIM-366840
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 16
Record ID
BIM-366840