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.

Functional Analysis

find a measer dense subset in r2

Functional Analysis

If f(x) = f(y) for every bounded linear functional f on a normed space X, show that x = y.

Functional Analysis

Let X be a normed space and X' its dual space. If X¢{O}, show that X' cannot be {O}.

Functional Analysis

show that if the endpoints of the circle in the above problem lie on the x-axis then the circular Arc must have a vertical tangent at the endpoints

Functional Analysis

show that the addition of the type dg/dx to the integrand function leaves the euler equation in the same form