
Recent Posts
 An inequality for functions on the plane
 Weighted isoperimetric inequalities in warped product manifolds
 FaberKrahn inequality
 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
Meta
Recent Comments
Lawrence G Mouille on Exponential maps of Lie g… 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… 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
 Complex analysis  Problem solving strategies.
 Lie groups with biinvariant Riemannian metric
 Sum of angle defects of polyhedrons
 Martingale Theory II: Conditional expectation
 Some integral formulas for hypersurface in Euclidean space 2
 Some integral formulas for hypersurface in Euclidean space
 An inequality for functions on the plane
 Surjectivity of Gauss map and its degree
 Weighted isoperimetric inequalities in warped product manifolds
 The discrete GaussBonnet theorem
Archives
Category Archives: Fourier analysis
Matrix multiplication as a convolution
1. The product of two power series/polynomials is The coefficients given by is sometimes called the Cauchy product. This is a convolution. 2. Let be a finite group and be the group algebra with complex coefficients. Let be two elements … Continue reading
Posted in Analysis, Fourier analysis, Linear Algebra
Tagged convolution, matrix multiplication
Leave a comment
Fourier coefficients as eigenvalues/spectrum
In this post I want to make a connection between Fourier coefficients and eigenvalues/spectrum. Let me put the claim up front: If , then is not invertible with respect to the convolution product. Please feel free to jump directly to … Continue reading
Posted in Fourier analysis, Linear Algebra
Tagged fourier coefficients, linear algebra
Leave a comment
Arithmetic progression in some subsets of $\mathbb{Z}_N$ (Part 2)
Last time I have mentioned the idea of the proof (of theorem 2). Now I continue and give a full detail here.
Posted in Fourier analysis, Number Theory
1 Comment
Arithmetic progression in some subsets of $\mathbb{Z}_N$ (Part 1)
This post is based mainly on the paper “Arithmetic progression in sumsets” by Ben Green, which talks about the length of arithmetic progressions of some special kind of subsets of , where is a sufficiently big odd prime. I will … Continue reading
Posted in Fourier analysis, Number Theory
Leave a comment
Fourier Analysis and Number Theory III: The Poisson summation formula as a trace formula
Yin and Yang are important concept in the Chinese philosophy. They usually describe two opposite things which are not only complement of each other but also have deep interrelationship. In mathematics, we called them duality. For example (1) primes vs … Continue reading
Posted in Fourier analysis, Number Theory
Leave a comment
Fourier Analysis and Number Theory II: The Poisson Summation Formula and The Functional Equation of The RiemannZeta Function
Riemann’s tenpagelong paper “Über die Anzahl der Primzahen unter einer gegebener Gröβe” has great influence on modern number theory. In the paper, he established two important properties of the Riemannzeta function (the summation is absolutely convergent for ).
Posted in Fourier analysis, Number Theory
Leave a comment
Fourier Analysis and Number theory I: The selfdual function e^{\pi x^2}
During a lecture at UCLA, Serge Lang asked what is the most important function in mathematics. This question is quite personal and every person certainly has his own opinion. In fact, a professor spoke out loud that the constant function … Continue reading
Posted in Fourier analysis, Number Theory
Leave a comment