Extensions of the Heisenberg-Weyl inequality
In this paper a number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove the n-dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2)...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1986-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000212 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564294314622976 |
|---|---|
| author | H. P. Heinig M. Smith |
| author_facet | H. P. Heinig M. Smith |
| author_sort | H. P. Heinig |
| collection | DOAJ |
| description | In this paper a number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove the n-dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2). From a general weighted form of the Hausdorff-Young theorem, a one-dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg-Weyl inequalities are given. |
| format | Article |
| id | doaj-art-cf816d7153174ff991e28005950ab517 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cf816d7153174ff991e28005950ab5172025-02-03T01:11:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019118519210.1155/S0161171286000212Extensions of the Heisenberg-Weyl inequalityH. P. Heinig0M. Smith1Department of Mathematical Sciences, McMaster University, Hamilton L8S 4K1, Ontario, CanadaDepartment of Mathematical Sciences, McMaster University, Hamilton L8S 4K1, Ontario, CanadaIn this paper a number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove the n-dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2). From a general weighted form of the Hausdorff-Young theorem, a one-dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg-Weyl inequalities are given.http://dx.doi.org/10.1155/S0161171286000212uncertainty inequalityFourier transformvarianceentropy Hausdorff-Young inequalityweighted norm inequalities. |
| spellingShingle | H. P. Heinig M. Smith Extensions of the Heisenberg-Weyl inequality International Journal of Mathematics and Mathematical Sciences uncertainty inequality Fourier transform variance entropy Hausdorff-Young inequality weighted norm inequalities. |
| title | Extensions of the Heisenberg-Weyl inequality |
| title_full | Extensions of the Heisenberg-Weyl inequality |
| title_fullStr | Extensions of the Heisenberg-Weyl inequality |
| title_full_unstemmed | Extensions of the Heisenberg-Weyl inequality |
| title_short | Extensions of the Heisenberg-Weyl inequality |
| title_sort | extensions of the heisenberg weyl inequality |
| topic | uncertainty inequality Fourier transform variance entropy Hausdorff-Young inequality weighted norm inequalities. |
| url | http://dx.doi.org/10.1155/S0161171286000212 |
| work_keys_str_mv | AT hpheinig extensionsoftheheisenbergweylinequality AT msmith extensionsoftheheisenbergweylinequality |