On Analog of Fourier Transform in Interior of the Light Cone
We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prov...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/685794 |
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| _version_ | 1832552422992510976 |
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| author | Tatyana Shtepina |
| author_facet | Tatyana Shtepina |
| author_sort | Tatyana Shtepina |
| collection | DOAJ |
| description | We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too. |
| format | Article |
| id | doaj-art-425a9e78c2534bb9ba675bc6f023dbb1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-425a9e78c2534bb9ba675bc6f023dbb12025-02-03T05:58:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/685794685794On Analog of Fourier Transform in Interior of the Light ConeTatyana Shtepina0Donetsk Institute of Municipal Economy, Bulavina Street 1, Donetsk 83053, UkraineWe introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.http://dx.doi.org/10.1155/2014/685794 |
| spellingShingle | Tatyana Shtepina On Analog of Fourier Transform in Interior of the Light Cone Abstract and Applied Analysis |
| title | On Analog of Fourier Transform in Interior of the Light Cone |
| title_full | On Analog of Fourier Transform in Interior of the Light Cone |
| title_fullStr | On Analog of Fourier Transform in Interior of the Light Cone |
| title_full_unstemmed | On Analog of Fourier Transform in Interior of the Light Cone |
| title_short | On Analog of Fourier Transform in Interior of the Light Cone |
| title_sort | on analog of fourier transform in interior of the light cone |
| url | http://dx.doi.org/10.1155/2014/685794 |
| work_keys_str_mv | AT tatyanashtepina onanalogoffouriertransformininteriorofthelightcone |