Annihilator concept and its application to best approximation theory

KAÇAR, AHMET; NASİBOV, Ferhad Hüseyinoğlu

Annihilator concept and its application to best approximation theory

Ferhad Hüseyinoğlu NASİBOV, (Kastamonu Üniversitesi, Fen Edebiyat Fakültesi, Fizik Bölümü, Kastamonu, Türkiye)

Ahmet KAÇAR (Kastamonu Üniversitesi, Eğitim Fakültesi, Kastamonu, Türkiye)

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

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Yıl: 2009 Cilt: 58 Sayı: 2 Sayfa Aralığı: 31 - 38 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022

Annihilator concept and its application to best approximation theory

Öz:

Konstrüktif fonksiyonlar teorisinde birbirinden farklı gibi görünen aslında ise aralarında sıkıbir bağlantı olan iki bölüm çok önemlidir: 1) Fonksiyonların en iyi yaklaşım teorisi, 2) Herhangi bir fonksiyon sınıfında tanımlı lineer fonksiyoneller için ekstremal problemler. Her ikisi de P. L. Chebyshev in temel olu¸sturan [2] çalı¸smasından başlayarak XX. yüzyılın ortalarına kadar serbest olarak geliştirildi ve kapsamlı, sistemli teoriler haline yükselebildi. Bu tarihten sonra da bu konular arasında mevcut olan ilişki fark edildi. Bu konular birbirleri ile irtibat halinde, paralel olarak, araştırılmaya başlandı. Sonuçta her iki problemde önemli sonuçlar elde edildi (S.M. Nikol- skiy, M.G Kreyin, S. Ya Havinson, G.Ts.Tumarkin, W. Rogosin sky) ([1], [4], [5], [11-13]). Böyle iki türden problemler arasında oluşturulan bağlantılara ikili (duality) ilişki adı verildi. Bu tür ikili ilişkilerde de sıfırlayan kavramı yer aldı ve önemli rol oynadı. Fakat bu tip bağlantılarda sıfırlayanlarılar incelenmedi, yapısıyla fazla ilgilenilmedi. Bu konuyda ilk olarak F. H. Nasibov i bazı fonksiyon sınıfarı için sıfırlayanların yapısınıbelirledi ve lineer problemlerin çözümünde uygulanabileceğini gösterdi ([6],[7],[8],[9],[10]). Bu makalede bu konuda elde ettiğimiz neticelerden bazıları sunulacaktır.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Öz:

In Constructive Theory of Functions , two sections that look dif ferent but in fact have strong relations are very important: 1) Theory of best approximation of functions and, 2) Extremal problems for linear functionals that defined in di¤erent function classes. Both of them studied independently started from the work [2] of P. L. Cheby shev and developed as systematic theories until the middle of 20th century. After that the relationship between these two theories has been realized and studied as connected theories. As a result, important findings for both prob lems obtained (S.M. Nikolskiy, M.G Kreyin, S. Ya Havinson, G.Ts.Tumarkin, W. Rogosinsky) ([1], [4], [5], [11-13]). Duality term coined for the relations between two problems such as these. In such duality relations, annihilator concept took place and played an important role. But no one studied or in- terested with the annihilator and its structure. F. H. Nasibov …rst one who studied and determined the annihilators structure, and showed how to use it to solve the linear extremal problems ([6],[7],[8],[9],[10]). In this paper, we will present our current …ndings about this topic.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Akhiyeser, N. I., Theory of Approximation, (1965), M. pp 1-408; Dover Publications, New York.
[2] Chebyshev, P. L., The theory of mechanisms known under the name of parallelograms, Complete Collected Works, Vol 2, M2, M.-4, (1947).
[3] İbragimov, I. I., Teoriya Priblijeniya Tsel{mi Funktsiyami, 1979, Baku, İzd. "ELM" NAN Azerbaijan Republic, 1–468, (In Russian).
[4] Khavinson, S.Ya., On an Extremal Problems of the Theory of Analytic Function, Usp Math. Nauk, V4, N4, Moscow, (1949), 158–159.
[5] Khavinson, S.Ya & Çatskaya, Ye, Ş., Dvoystvenniye Sootno¸seniya i Kriterii Elementov Nailuç¸sego Priblijeniya, MİSİ, Moscow, (1976), (In Russian).
[6] Nasibov, F. G., Annulyator Klassa W;z u Nekotor{ye Primeneniya, VİNİTİ, No 1671-82, Dep. (1982), 1-11, Moscow, (In Russian).
[7] Nasibov, F. G., Description of Annihilator of one Class of Entire Functions of Finite Semi- Order and Some Applications, ·Izv. VUZ SSSR, MATEMATİKA, V. 30, N 2, (1986), 29–33.
[8] Nasibov, F. G., Extremal Problems in Classes of Entire Functions Bounded on the Real Axis, İzv. VUZ SSSR, V44, N10, (2000), 45–52, Allerton Press, New York.
[9] Nasibov, F. G., K Extremaln{m Problemam v Klassakh Tselıkh Funktsiy, Dokl. NAN Azer- baijan Republic, V62, N5–6, (2006), 26–32, (In Russian).
[10] Nasibov, F. G., Extremalnıye Zadachi v Klassakh Tselıkh Funktsiy, , ·Izd. "ELM" NAN Azerbaijan Republic, (1998), 1–298, Baku, (In Russian).
[11] Natanson, I. P., Konstruktivnaya Teoriya Funktsiy, 1949, Moskova, 1-688. (In Russian)
[12] Timan, A. F., Teoriya Priblijeniya Funktsiy Deystvitelnogo Peremenogo, 1960, Moscow, (In Russian). (Theory of Approximation of Functions of a Real Variable, Dover Publ., INC, New York, 1963).
[13] Zinger, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, 1970, Berlin, Springer

APA	NASİBOV F, KAÇAR A (2009). Annihilator concept and its application to best approximation theory. , 31 - 38.
Chicago	NASİBOV Ferhad Hüseyinoğlu,KAÇAR AHMET Annihilator concept and its application to best approximation theory. (2009): 31 - 38.
MLA	NASİBOV Ferhad Hüseyinoğlu,KAÇAR AHMET Annihilator concept and its application to best approximation theory. , 2009, ss.31 - 38.
AMA	NASİBOV F,KAÇAR A Annihilator concept and its application to best approximation theory. . 2009; 31 - 38.
Vancouver	NASİBOV F,KAÇAR A Annihilator concept and its application to best approximation theory. . 2009; 31 - 38.
IEEE	NASİBOV F,KAÇAR A "Annihilator concept and its application to best approximation theory." , ss.31 - 38, 2009.
ISNAD	NASİBOV, Ferhad Hüseyinoğlu - KAÇAR, AHMET. "Annihilator concept and its application to best approximation theory". (2009), 31-38.

APA	NASİBOV F, KAÇAR A (2009). Annihilator concept and its application to best approximation theory. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 58(2), 31 - 38.
Chicago	NASİBOV Ferhad Hüseyinoğlu,KAÇAR AHMET Annihilator concept and its application to best approximation theory. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 58, no.2 (2009): 31 - 38.
MLA	NASİBOV Ferhad Hüseyinoğlu,KAÇAR AHMET Annihilator concept and its application to best approximation theory. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.58, no.2, 2009, ss.31 - 38.
AMA	NASİBOV F,KAÇAR A Annihilator concept and its application to best approximation theory. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2009; 58(2): 31 - 38.
Vancouver	NASİBOV F,KAÇAR A Annihilator concept and its application to best approximation theory. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2009; 58(2): 31 - 38.
IEEE	NASİBOV F,KAÇAR A "Annihilator concept and its application to best approximation theory." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 58, ss.31 - 38, 2009.
ISNAD	NASİBOV, Ferhad Hüseyinoğlu - KAÇAR, AHMET. "Annihilator concept and its application to best approximation theory". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 58/2 (2009), 31-38.