MATHEMATICS DEPARTMENT STANFORD UNIVERSITY
MATH 175 SPRING 2013 HOMEWORK 1
DUE AT LECTURE FRIDAY APRIL 12
1. For a sequence of real numbers x = (xi )N we dene for p > 0
1
p
x
p
|xi |p
:=
.
i=1
(a) (4
MATHEMATICS DEPARTMENT STANFORD UNIVERSITY
MATH 175 SPRING 2013 HOMEWORK 3
DUE AT LECTURE FRIDAY APRIL 26
1. Let U R be open. We consider the space L1 (U ) of functions f : U R satisfying
f
L1 (U )
|f
MATHEMATICS DEPARTMENT STANFORD UNIVERSITY
MATH 175 SPRING 2013 HOMEWORK 4
DUE AT LECTURE FRIDAY MAY 3
1. Consider the space of continuous functions C 0 ([1, 1]) with the norm f
Let U C 0 ([1, 1]) be
MATHEMATICS DEPARTMENT STANFORD UNIVERSITY
MATH 175 SPRING 2013 HOMEWORK 2
DUE AT LECTURE FRIDAY APRIL 19
1. We consider the function space
M := cfw_f : [1, 1] R | f smooth and f (1) = 0
and the inner
MATHEMATICS DEPARTMENT STANFORD UNIVERSITY
MATH 175 SPRING 2013 HOMEWORK 7
DUE AT LECTURE FRIDAY MAY 31
1. Let V and W be Hilbert spaces, (ek )kN a complete orthonormal system of V and
(fk )kN an orth