
Recent Posts
 Why is a² + b² ≥ 2ab ?
 A remark on the divergence theorem
 The CauchySchwarz inequality and the Lagrange identity
 On the existence of a metric compatible with a given connection
 A curious identity on the median triangle
 27 lines on a smooth cubic surface
 Weighted HsiungMinkowski formulas and rigidity of umbilic hypersurfaces
 The discrete GaussBonnet theorem
 Why a vector field rotates about its curl?
 A functional inequality on the boundary of static manifolds
Meta
Recent Comments
tong cheung yu on On the existence of a metric c… Marco Barchiesi on Simple curves with a positive… tong cheung yu on Toric perspective 1 lamwk on Why is a² + b² ≥ 2ab ? Maurice OReilly on Spherical cosine law KKK on Sobolev and Isoperimetric… Anonymous on Sobolev and Isoperimetric… tong cheung yu on On the existence of a metric c… Anonymous on Closed subspaces of a reflexiv… KKK on A curious identity on the medi… Categories
 Algebra
 Algebraic geometry
 Analysis
 Applied mathematics
 Calculus
 Combinatorics
 Complex analysis
 Differential equations
 Discrete Mathematics
 Dynamical system
 Fourier analysis
 Functional analysis
 General Relativity
 Geometry
 Group theory
 Inequalities
 Linear Algebra
 Miscellaneous
 Number Theory
 Operator Theory
 Optimization
 Potential theory
 Probability
 Set Theory
 Statistics
 Topology
 Uncategorized
Top Posts
Archives
Category Archives: Functional analysis
Weak L^1 is not locally convex
Let be the Lebesgue measure on . Consider , the space of Lebesgue measurable functions for which there exists some constant such that for every , . The purpose of this post is to show that this is not a … Continue reading
Posted in Functional analysis
Leave a comment
Fourier transform of tempered distributions
This is an extension to my previous post A short note about tempered distributions. Our objective is to discuss the Fourier transform of distributions and give some “little” applications. Before that let us review some basics. We shall use the … Continue reading
Posted in Analysis, Functional analysis
1 Comment
A short note about tempered distributions
Recently I am doing distributions theory, this notes is for filling small gaps and showing some “applications”. I should put some definitions at the top to make this article selfcontaining. Unfortunately I do not have much time, so I go … Continue reading
Posted in Functional analysis
Leave a comment
A chain of double duals
Let X be a Banach space. We know that X embeds into its double dual X** as a closed subspace isometrically via defined by and we say that X is reflexive if this embedding is a surjection. One may continue … Continue reading
Posted in Functional analysis
4 Comments
Dual norm in R^n
I shall start posting some homework solutions that readers may be interested. This post discusses one special property about the Euclidean norm. Let be a norm on . By identifying with its usual Euclidean inner product, we can study the … Continue reading
Posted in Functional analysis, Linear Algebra
2 Comments
Closed Graph Theorem implies Open Mapping Theorem
Today Wongting raised the question in the real analysis prelims at UW about proving that the Closed Graph Theorem (CGT) implies the Open Mapping Theorem (OMT). This is a standard exercise in the first course of functional analysis. Let us … Continue reading
Posted in Analysis, Functional analysis
3 Comments
Exercises in Real Analysis II
This post is a sequel to Exercises in Real Analysis. 4. Let be the triangle , and be the restriction of the planar Lebesgue measure on . Suppose that . Prove that . Solution. Assume on the contrary that . … Continue reading
Posted in Analysis, Functional analysis
2 Comments