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Dirichlet's principle, also known as Thomson's principle, states that there exists a function u that minimizes the functional D[u]=int_Omega|del u|^2dV (called the Dirichlet ...

A.k.a. the pigeonhole principle. Given n boxes and m>n objects, at least one box must contain more than one object. This statement has important applications in number theory ...

A loose term for a true statement which may be a postulate, theorem, etc.

There are several types of integrals which go under the name of a "Dirichlet integral." The integral D[u]=int_Omega|del u|^2dV (1) appears in Dirichlet's principle. The ...

A Dirichlet L-series is a series of the form L_k(s,chi)=sum_(n=1)^inftychi_k(n)n^(-s), (1) where the number theoretic character chi_k(n) is an integer function with period k, ...

The Dirichlet kernel D_n^M is obtained by integrating the number theoretic character e^(i<xi,x>) over the ball |xi|<=M, D_n^M=-1/(2pir)d/(dr)D_(n-2)^M.

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

Let h be a real-valued harmonic function on a bounded domain Omega, then the Dirichlet energy is defined as int_Omega|del h|^2dx, where del is the gradient.