An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces
Consider the space 𝐿2(ℂ,𝑑𝜇(𝑧)), where 𝑑𝜇(𝑧)=𝑒−|𝑧|2⋀𝑑𝑑𝑧𝑧 is the Gaussian measure, and its generalized Bargmann subspaces 𝐸𝑚 which are the null kernels of the operator Δ=−𝜕2/𝜕𝑧𝜕𝑧+𝑧(𝜕/𝜕𝑧)−𝑚𝐼; 𝑚=0,1,…. In this work, we present an other construction of 𝐸𝑚 following the Hermite functions which all...
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| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/357050 |
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| author | Abdelkader Intissar |
| author_facet | Abdelkader Intissar |
| author_sort | Abdelkader Intissar |
| collection | DOAJ |
| description | Consider the space 𝐿2(ℂ,𝑑𝜇(𝑧)), where 𝑑𝜇(𝑧)=𝑒−|𝑧|2⋀𝑑𝑑𝑧𝑧 is the
Gaussian measure, and its generalized Bargmann subspaces 𝐸𝑚 which are the null
kernels of the operator Δ=−𝜕2/𝜕𝑧𝜕𝑧+𝑧(𝜕/𝜕𝑧)−𝑚𝐼;
𝑚=0,1,…. In this work, we present an other construction of 𝐸𝑚 following the Hermite functions
which allows us to define a family of generalized Bargmann transform 𝐵𝑚 which maps isometrically 𝐸𝑚 into 𝐿2(ℝ). The generalized coherent states ∣𝑧⟩𝑚 associated to 𝐸𝑚 are constructed and some properties of them are given. |
| format | Article |
| id | doaj-art-9fcaef621bec4f938d3cef42051749b3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9fcaef621bec4f938d3cef42051749b32025-08-20T03:38:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/357050357050An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann SpacesAbdelkader Intissar0Equipe d'Analyse spectrale, UMR-CNRS n : 6134, Université de Corse, Quartier Grossetti, 20 250 Corté, FranceConsider the space 𝐿2(ℂ,𝑑𝜇(𝑧)), where 𝑑𝜇(𝑧)=𝑒−|𝑧|2⋀𝑑𝑑𝑧𝑧 is the Gaussian measure, and its generalized Bargmann subspaces 𝐸𝑚 which are the null kernels of the operator Δ=−𝜕2/𝜕𝑧𝜕𝑧+𝑧(𝜕/𝜕𝑧)−𝑚𝐼; 𝑚=0,1,…. In this work, we present an other construction of 𝐸𝑚 following the Hermite functions which allows us to define a family of generalized Bargmann transform 𝐵𝑚 which maps isometrically 𝐸𝑚 into 𝐿2(ℝ). The generalized coherent states ∣𝑧⟩𝑚 associated to 𝐸𝑚 are constructed and some properties of them are given.http://dx.doi.org/10.1155/2010/357050 |
| spellingShingle | Abdelkader Intissar An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces International Journal of Mathematics and Mathematical Sciences |
| title | An Elementary Construction on Nonlinear Coherent States Associated
to Generalized Bargmann Spaces |
| title_full | An Elementary Construction on Nonlinear Coherent States Associated
to Generalized Bargmann Spaces |
| title_fullStr | An Elementary Construction on Nonlinear Coherent States Associated
to Generalized Bargmann Spaces |
| title_full_unstemmed | An Elementary Construction on Nonlinear Coherent States Associated
to Generalized Bargmann Spaces |
| title_short | An Elementary Construction on Nonlinear Coherent States Associated
to Generalized Bargmann Spaces |
| title_sort | elementary construction on nonlinear coherent states associated to generalized bargmann spaces |
| url | http://dx.doi.org/10.1155/2010/357050 |
| work_keys_str_mv | AT abdelkaderintissar anelementaryconstructiononnonlinearcoherentstatesassociatedtogeneralizedbargmannspaces AT abdelkaderintissar elementaryconstructiononnonlinearcoherentstatesassociatedtogeneralizedbargmannspaces |