3. Let K(r, y) = xy(x+ y), 0 < x,y <1 and consider the following operator K K f(y) = | K(y, 1)f(r)dx. %3D a) Is this operator bounded as an operator acting from L'(0, 1) into itself? b) Is K bounded as an operator acting from L (0, 1) into L'(0, 1)? c) Is K bounded as an operator acting on L²(0, 1)?

3. Let K(r, y) = xy(x+ y), 0 < x,y <1 and consider the following operator K K f(y) = | K(y, 1)f(r)dx. %3D a) Is this operator bounded as an operator acting from L'(0, 1) into itself? b) Is K bounded as an operator acting from L (0, 1) into L'(0, 1)? c) Is K bounded as an operator acting on L²(0, 1)?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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