caa a22 4500 388023694 CHVBK 20180307124931.0 cr unu---uuuuu 161130e199802 xx s 000 0 eng 10.1017/S001309150001943X doi S001309150001943X pii (NATIONALLICENCE)cambridge-10.1017/S001309150001943X Construction of Schauder decomposition on banach spaces of periodic functions [Elektronische Daten] This paper deals with Schauder decompositions of Banach spaces X2π of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1, , which form a multiresolution of X2π,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C2π on the other. The approach, using "orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X2π and a biorthogonal system for X2π, and its dual X2π. Decomposition and reconstruction algorithms are derived from the construction. Copyright © Edinburgh Mathematical Society 1998 Goh Say Song Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore Lee S. L. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore Shen Zuowei Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore Tang W. S. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore Proceedings of the Edinburgh Mathematical Society Cambridge University Press 41/1(1998-02), 61-91 0013-0915 41:1<61 1998 41 PEM https://doi.org/10.1017/S001309150001943X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S001309150001943X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goh Say Song Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore NATIONALLICENCE 700 1- Lee S. L. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore NATIONALLICENCE 700 1- Shen Zuowei Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore NATIONALLICENCE 700 1- Tang W. S. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore NATIONALLICENCE 773 0- Proceedings of the Edinburgh Mathematical Society Cambridge University Press 41/1(1998-02), 61-91 0013-0915 41:1<61 1998 41 PEM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge