Functional Equations and Linear Transformations I (Solvability on Lp Spaces)

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Authors

  • B. P. Duggal
     Makerere University, P. O. Box 7062, Kampala ,UG

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)).

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Published

1974-12-01

How to Cite

Duggal, B. P. (1974). Functional Equations and Linear Transformations I (Solvability on L<sub>p</sub> Spaces). The Journal of the Indian Mathematical Society, 38(1-4), 71–97. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/16683

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 B. P. Duggal

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

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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.

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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.