Search Results for ""

Any complex measure lambda decomposes into an absolutely continuous measure lambda_a and a singular measure lambda_c, with respect to some positive measure mu. This is the ...

Let x:p(x)->xp(x), then for any operator T, T^'=Tx-xT is called the Pincherle derivative of T. If T is a shift-invariant operator, then its Pincherle derivative is also a ...

The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

That portion of mathematics dealing with functions of real variables. While this includes some portions of topology, it is most commonly used to distinguish that portion of ...

An operator E such that E^ap(x)=p(x+a).

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

The proof theories of propositional calculus and first-order logic are often referred to as classical logic. Intuitionistic propositional logic can be described as classical ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.