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Functional Analysis
If a sub additive functional defined on a normed space X is nonnegative outside a sphere {x Illxll = r}, show that it is nonnegative for all x E X
Functional Analysis
prove that a finite partially ordered set A has at least one maximal element
Functional Analysis
Please, this is urgent , solve it as soon as possible.
Suppose V is finite-dimensional and phi is a linear functional on V. Then
there is a unique vector u in V such that
phi(v)=< v, u> for every v in V.
Suppose V is finite-dimensional and phi is a linear functional on V. Then
there is a unique vector u in V such that
phi(v)=< v, u> for every v in V.
Functional Analysis
Show that norm is continuous function.
Functional Analysis
prove that
||u||>0 for u<>0
Functional Analysis
A metric space M is called a сomplete metric space if
Functional Analysis
Let TES^1. Prove that for all φES, (T*φ)^ = (2π)^(n/2)(φ-hat)(T-hat).
Functional Analysis
Let TES^1. Prove that for all φES, (T*φ)^ = (2π)^(n/2)(φ-hat)(T-hat).
Functional Analysis
Let TES^1. Prove that for all multi-indices a, (D^(a)T)^ = x^(a)T-hat.
Functional Analysis
Let T be a tempered distribution. Then for all multi-indices a, we define ∂^(a)T to be the linear functional on S by (∂^(a)T)(φ) = (-1)^(|a|)T(∂^(a)φ), φES. Prove that ∂^(a)T is a tempered distribution.
