A trigonometric orthogonality with respect to a nonnegative Borel measure
Apstrakt
In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semi- integer degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.
Ključne reči:
trigonometric polynomial of semi-integer degree / reproducing kernel / orthogonality / nonnegative Borel measure / Fourier series / Christoffel functionIzvor:
Filomat, 2012, 26, 4, 689-696Izdavač:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Finansiranje / projekti:
- Aproksimacija integralnih i diferencijalnih operatora i primene (RS-MESTD-Basic Research (BR or ON)-174015)
- Razvoj novih informaciono-komunikacionih tehnologija, korišćenjem naprednih matematičkih metoda, sa primenama u medicini, telekomunikacijama, energetici, zaštititi nacionalne baštine i obrazovanju (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-44006)
DOI: 10.2298/FIL1204689M
ISSN: 0354-5180
WoS: 000322023300007
Scopus: 2-s2.0-84867583604
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir V. AU - Cvetković, Aleksandar AU - Stanić, Marija P. PY - 2012 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1472 AB - In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semi- integer degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - A trigonometric orthogonality with respect to a nonnegative Borel measure EP - 696 IS - 4 SP - 689 VL - 26 DO - 10.2298/FIL1204689M ER -
@article{ author = "Milovanović, Gradimir V. and Cvetković, Aleksandar and Stanić, Marija P.", year = "2012", abstract = "In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semi- integer degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "A trigonometric orthogonality with respect to a nonnegative Borel measure", pages = "696-689", number = "4", volume = "26", doi = "10.2298/FIL1204689M" }
Milovanović, G. V., Cvetković, A.,& Stanić, M. P.. (2012). A trigonometric orthogonality with respect to a nonnegative Borel measure. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 26(4), 689-696. https://doi.org/10.2298/FIL1204689M
Milovanović GV, Cvetković A, Stanić MP. A trigonometric orthogonality with respect to a nonnegative Borel measure. in Filomat. 2012;26(4):689-696. doi:10.2298/FIL1204689M .
Milovanović, Gradimir V., Cvetković, Aleksandar, Stanić, Marija P., "A trigonometric orthogonality with respect to a nonnegative Borel measure" in Filomat, 26, no. 4 (2012):689-696, https://doi.org/10.2298/FIL1204689M . .