Functional Equations and Linear Transformations I (Solvability on Lp Spaces)
Abstract
Let A = A(X) be a space of functions defined on a set X. A transformation W on A which is linear, in the purely algebraic sense, and has the property that the values of the transform Wf of an element f ∈ A at a point x ∈ X depends solely on the value of f at some other point x' ∈ X is given by the formula (Wf)(x) = Q(x)f(V(x)).Downloads
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Copyright (c) 1974 B. P. Duggal
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References
COOPER, J.L.B., "Functional equations for linear transformations", Proc. Lond. Math. Soc, 20 (1970), 1-32.
DUGGAL, B.P., Ph. D. Thesis, London University (England), 1971.
HARDY, G.H., LITTLEWOOD, J. E. AND P'OLYA, G., Inequalities, Cambridge (1934).
HEWITT, E. AND STROMBERG, K., Real and Abstract Analysis, Springer-Verlag (1965).
HILLE, E. AND PHILLIPS, R.S., Functional Analysis and Semigroups, Providence, R.I. (1957).
HSRMANDER, L., "Estimates for translation invariant operators in LP", Acta Math. 104 (1960), 93-140.
KOBER, H., "On functional equations and bounded linear transformations", Proc. Lond. Math. Soc. 14 (1964), 495-519.
OKIKIOLU, G.O., Aspects of the theory of bounded integral operator s on LPspaces, Academic Press (1971).
"On certain bounded linear transformations in LP", Proc. Lond Math. Soc, 17 (1967), 700-14.
"On fundamental operators in Lf and certain of their applications", Am. Jnl. of Math., 90(1968), 1074-1102.
PLANCHEREL, M., "Quelques remarques a propos d'une note de G.H. Hardy: The resultant of two Fourier kernels", Proc. Camb. Phil. Soc, 33 (1937) 413-18.
WALSH, T., "On Z." estimates for integral transformations", Trans. Am. Math. Soc, 155(1971), 195-215.