Fourier transforms in generalized Fock spaces
A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…),where ϕ0∈C and ϕq∈L2(R3q), q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expandi...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000655 |
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| _version_ | 1832558584474370048 |
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| author | John Schmeelk |
| author_facet | John Schmeelk |
| author_sort | John Schmeelk |
| collection | DOAJ |
| description | A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…),where ϕ0∈C and ϕq∈L2(R3q), q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces. |
| format | Article |
| id | doaj-art-4e11858cab6f4dacbd2d3d182d731972 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4e11858cab6f4dacbd2d3d182d7319722025-02-03T01:32:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113343144110.1155/S0161171290000655Fourier transforms in generalized Fock spacesJohn Schmeelk0Department of Mathematical Sciences, Box 2014, Oliver Hall, 1015 W. Main Street, Virginia Commonwealth University, Richmond 23284-2014, VA, USAA classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…),where ϕ0∈C and ϕq∈L2(R3q), q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.http://dx.doi.org/10.1155/S0161171290000655generalized Fock sapcestempered distributionsFourier transformsand rapid descent test functions. |
| spellingShingle | John Schmeelk Fourier transforms in generalized Fock spaces International Journal of Mathematics and Mathematical Sciences generalized Fock sapces tempered distributions Fourier transforms and rapid descent test functions. |
| title | Fourier transforms in generalized Fock spaces |
| title_full | Fourier transforms in generalized Fock spaces |
| title_fullStr | Fourier transforms in generalized Fock spaces |
| title_full_unstemmed | Fourier transforms in generalized Fock spaces |
| title_short | Fourier transforms in generalized Fock spaces |
| title_sort | fourier transforms in generalized fock spaces |
| topic | generalized Fock sapces tempered distributions Fourier transforms and rapid descent test functions. |
| url | http://dx.doi.org/10.1155/S0161171290000655 |
| work_keys_str_mv | AT johnschmeelk fouriertransformsingeneralizedfockspaces |