• Exercise 5 For g E C[0, 1] define f(s) = | e-"g(t) dt, se [0, 1). S E Assuming that for all t E [0, 1] the function e-st is a continuous function of the variable s prove that ||f|| < ||9||, where || || is the standard norm in C[0, 1], i.e. ||f|| = max,e(0,1] |f(s)|.
• Exercise 5 For g E C[0, 1] define f(s) = | e-"g(t) dt, se [0, 1). S E Assuming that for all t E [0, 1] the function e-st is a continuous function of the variable s prove that ||f|| < ||9||, where || || is the standard norm in C[0, 1], i.e. ||f|| = max,e(0,1] |f(s)|.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Exercise 5 For g E C[0, 1] define
1
f(e) = |e*g(t) dt,
= /
-st
sE [0, 1].
Assuming that for all t e [0, 1] the function e-st is a continuous function of the variable s prove
that ||f || < ||g|l, where || · || is the standard norm in C[0, 1], i.e. || f|| = maxsE[0,1]| |f(s)|.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44d4bb1e-783f-43e8-9cab-fd5fb3199e14%2F3d52ae3c-0104-4ef1-83f0-bb5d880755da%2Fxt1hfup_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 5 For g E C[0, 1] define
1
f(e) = |e*g(t) dt,
= /
-st
sE [0, 1].
Assuming that for all t e [0, 1] the function e-st is a continuous function of the variable s prove
that ||f || < ||g|l, where || · || is the standard norm in C[0, 1], i.e. || f|| = maxsE[0,1]| |f(s)|.
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