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Almost-Periodic Functions and Functional Equations by Luigi Amerio, Giovanni Prouse (auth.) is a nonfiction available to read on EtoBox.

What is Almost-Periodic Functions and Functional Equations about?

Let t' be an arbitrary point of J. In the interval -t'f--- ° arbitrarily and choose ne in such a way that sup Ilf(t) -fn,(t) I I :$ e. ## J Let T be an e-a.p. for fn,(t). Then, "It E J, 11f(t+ T) -f{t) I I :$ Ilf(t+ T) -fn,(t+ T) I I + Ilfn,{t+ T) -fn,(t) I I + Ilfn,(t) -f(t) I I :$ 3e, that is, T is a 3e-a.p\_ for f(t)- As the derivative f'(t) is u.c. there exists, "Ie> 0, a oe > ° such that, Vt" and t', with It" -t'l:$ 0., we have 11f'(t")-f'(t')11 :$ e\_ Furthermore, Vt E J and for (l/n):$ e, that is, the sequence of a.p. functions n(f(t+ (lin» -f(t» converges uniformly to f'(t). The thesis then follows from theorem V. VII. x=f(t) X-a.p., y=g(x) with values in Y (Banach space) and continuous on Bff(t) => g(f(t» Y-a.p.

Who reads Almost-Periodic Functions and Functional Equations?

Author

Luigi Amerio, Giovanni Prouse (auth.)

Publisher

Springer-Verlag New York

Published

1971

Language

EN

ISBN

9781475712544

Category

nonfiction

Subjects

Mathematics, Stem