Unitary operatorIn functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces. A unitary element is a generalization of a unitary operator. In a unital algebra, an element U of the algebra is called a unitary element if UU = UU = I, where I is the identity element. Definition 1.
Self-adjoint operatorIn mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map A (from V to itself) that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian matrix, i.e., equal to its conjugate transpose A^∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers.
LC circuitFile:LC parallel simple.svg|LC circuit diagram File:Low cost DCF77 receiver.jpg|LC circuit ''(left)'' consisting of ferrite coil and capacitor used as a tuned circuit in the receiver for a [[radio clock]] File:Tuned circuit of shortwave radio transmitter from 1938.jpg|Output tuned circuit of [[shortwave]] [[radio transmitter]] An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together.
Continuous linear operatorIn functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator if and only if it is a continuous linear operator. Continuous function (topology) and Discontinuous linear map Bounded operator Suppose that is a linear operator between two topological vector spaces (TVSs). The following are equivalent: is continuous.
Fourier transformIn physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
