Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space
This research work places a new and consistent inner product <.,.>p on a countable family of the real Lp function spaces, proves generalizations of some of the inequalities of the classical inner product for <.,.>p provides a construction of a species of Higher Orthogonal Polynomials in...
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| Rochtain ar líne: | http://localhost:8080/xmlui/handle/123456789/3501 |
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| _version_ | 1810764569991184384 |
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| author | Oyadare, 'Femi O. |
| author_facet | Oyadare, 'Femi O. |
| author_sort | Oyadare, 'Femi O. |
| collection | DSpace |
| description | This research work places a new and consistent inner product <.,.>p on a countable family of the real Lp function spaces, proves generalizations of some of the inequalities of the classical inner product for <.,.>p provides a construction of a species of Higher Orthogonal Polynomials in these inner-product-admissible function spaces, and ultimately brings us to a study of the Generalized Fourier Series Expansion in terms of these polynomials. First, the reputation of this new inner product is established by the proofs of various inequalities and identities, all of which are found to be generalizations of the classical inequalities of functional analysis. Thereafter two orthogonalities of <.,.>p which coincide at p = 2) are defined while the Gram-Schmidt orthonormalization procedure is considered and lifted to accommodate this product, out of which emerges a set of higher orthogonal polynomials in Lp{-1, 1} that reduce to the Legendre Polynomials at p = 2. We argue that this inner product provides a formidable tool for the investigation of Harmonic Analysis on the real Lp function spaces for p other than p = 2, and a revisit of the various fields where the theory of inner product spaces is indispensable is recommended for further studies. |
| format | Article |
| id | oai:ir.oauife.edu.ng:123456789-3501 |
| institution | My University |
| language | English |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oai:ir.oauife.edu.ng:123456789-35012023-05-13T11:10:43Z Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space Oyadare, 'Femi O. Orthogonalities Elementary vector algebra Vector Orthogonality This research work places a new and consistent inner product <.,.>p on a countable family of the real Lp function spaces, proves generalizations of some of the inequalities of the classical inner product for <.,.>p provides a construction of a species of Higher Orthogonal Polynomials in these inner-product-admissible function spaces, and ultimately brings us to a study of the Generalized Fourier Series Expansion in terms of these polynomials. First, the reputation of this new inner product is established by the proofs of various inequalities and identities, all of which are found to be generalizations of the classical inequalities of functional analysis. Thereafter two orthogonalities of <.,.>p which coincide at p = 2) are defined while the Gram-Schmidt orthonormalization procedure is considered and lifted to accommodate this product, out of which emerges a set of higher orthogonal polynomials in Lp{-1, 1} that reduce to the Legendre Polynomials at p = 2. We argue that this inner product provides a formidable tool for the investigation of Harmonic Analysis on the real Lp function spaces for p other than p = 2, and a revisit of the various fields where the theory of inner product spaces is indispensable is recommended for further studies. 2014-10-23T09:09:00Z 2018-10-29T11:15:47Z 2014-10-23T09:09:00Z 2018-10-29T11:15:47Z 2005 Article Oyadare, 'Femi O. (2005). Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space. American Journal of Undergraduate Research, 4(3) http://localhost:8080/xmlui/handle/123456789/3501 en PDF application/pdf |
| spellingShingle | Orthogonalities Elementary vector algebra Vector Orthogonality Oyadare, 'Femi O. Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space |
| title | Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space |
| title_full | Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space |
| title_fullStr | Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space |
| title_full_unstemmed | Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space |
| title_short | Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space |
| title_sort | construction of higher orthogonal polynomials through a new inner product p in a countable real lp space |
| topic | Orthogonalities Elementary vector algebra Vector Orthogonality |
| url | http://localhost:8080/xmlui/handle/123456789/3501 |
| work_keys_str_mv | AT oyadarefemio constructionofhigherorthogonalpolynomialsthroughanewinnerproductpinacountablereallpspace |