Suppose that f: (0, ) R is continuous and bounded and that £{f} exists at some a
Question:
a) Prove that
for all N N.
b) Prove that the integral «0 e-(s-a)t(ɸ)(t)dt converges uniformly on [b, ) for any b > a and
c) Prove that £{f} exists, is continuous on (a, ), and satisfies
d) Let g(t) = tf(t) for t (0, ). Prove that £{f} is differentiate on (a, ) and
for all s (a, ).
e) If, in addition, fʹ is continuous and bounded on (0, ), prove that
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