Positive definiteness: from scalar to operator-valued kernels
In this paper we present a short overview of results that provide relationships among scalar, matrix-valued and certain operator-valued positive definite kernels. We refine and extend some of them in order that they may be applied for strict positive definiteness as well. This is a topic not well ex...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2021-12-01
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| Series: | Surveys in Mathematics and its Applications |
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| Online Access: | https://www.utgjiu.ro/math/sma/v16/p16_19.pdf |
| _version_ | 1818051229588127744 |
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| author | V. A. Menegatto |
| author_facet | V. A. Menegatto |
| author_sort | V. A. Menegatto |
| collection | DOAJ |
| description | In this paper we present a short overview of results that provide relationships among scalar, matrix-valued and certain operator-valued positive definite kernels. We refine and extend some of them in order that they may be applied for strict positive definiteness as well. This is a topic not well explored in the literature but that has potential usefulness in the characterization of several classes of positive definite and strictly positive definite kernels. This is ratified in the paper with the inclusion of a number of applications and examples. |
| first_indexed | 2024-12-10T11:06:03Z |
| format | Article |
| id | doaj.art-7d4d1037e3a24b5ba80f26ad6f1ce9e7 |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-12-10T11:06:03Z |
| publishDate | 2021-12-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-7d4d1037e3a24b5ba80f26ad6f1ce9e72022-12-22T01:51:33ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982021-12-0116 (2021)339359Positive definiteness: from scalar to operator-valued kernelsV. A. Menegatto 0Departamento de Matemática -ICMC Universidade de São Paulo 13560-970 São Carlos SP Brazil Current Affiliation: Departamento de Matemática - ICE Universidade Federal de Juiz de Fora 36036-330 Juiz de Fora MG BrazilIn this paper we present a short overview of results that provide relationships among scalar, matrix-valued and certain operator-valued positive definite kernels. We refine and extend some of them in order that they may be applied for strict positive definiteness as well. This is a topic not well explored in the literature but that has potential usefulness in the characterization of several classes of positive definite and strictly positive definite kernels. This is ratified in the paper with the inclusion of a number of applications and examples. https://www.utgjiu.ro/math/sma/v16/p16_19.pdfpositive definitenessstrict positive definitenessscalar kernelsmatrix-valued kernelsoperator-valued kernels |
| spellingShingle | V. A. Menegatto Positive definiteness: from scalar to operator-valued kernels Surveys in Mathematics and its Applications positive definiteness strict positive definiteness scalar kernels matrix-valued kernels operator-valued kernels |
| title | Positive definiteness: from scalar to operator-valued kernels |
| title_full | Positive definiteness: from scalar to operator-valued kernels |
| title_fullStr | Positive definiteness: from scalar to operator-valued kernels |
| title_full_unstemmed | Positive definiteness: from scalar to operator-valued kernels |
| title_short | Positive definiteness: from scalar to operator-valued kernels |
| title_sort | positive definiteness from scalar to operator valued kernels |
| topic | positive definiteness strict positive definiteness scalar kernels matrix-valued kernels operator-valued kernels |
| url | https://www.utgjiu.ro/math/sma/v16/p16_19.pdf |
| work_keys_str_mv | AT vamenegatto positivedefinitenessfromscalartooperatorvaluedkernels |