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60 relations: Abel transform, Banach space, Bateman transform, Characteristic equation (calculus), Circulant matrix, Circular convolution, Compact operator, Convolution, Cyclic group, Differential equation, Domain of a function, Eigenvalues and eigenvectors, Electronics, Fourier series, Fourier transform, Fredholm kernel, Fredholm operator, Fredholm theory, Frequency domain, Function (mathematics), Generalized function, Hankel transform, Hartley transform, Hermite transform, Hilbert transform, Integral equation, Integro-differential equation, Inverse Laplace transform, Jacobi transform, Kernel (statistics), Kernel method, Laguerre transform, Laplace transform, Legendre transform, Line integral, Linear map, List of Fourier-related transforms, List of mathematic operators, List of transforms, Mathematics, Mellin transform, Nachbin's theorem, Nuclear operator, Operator (mathematics), Orthonormal basis, Permutation, Poisson kernel, Propagator, Reproducing kernel Hilbert space, Schwartz kernel theorem, ..., Sine, Sine and cosine transforms, Stochastic discount factor, Symbolic integration, Time domain, Trigonometric functions, Two-sided Laplace transform, Variable (mathematics), Voltage, Weierstrass transform. Expand index (10 more) »
Abel transform
In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Bateman transform
In the mathematical study of partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables.
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Characteristic equation (calculus)
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given n\,th-order differential equation or difference equation.
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Circulant matrix
In linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector.
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Circular convolution
The circular convolution, also known as cyclic convolution, of two aperiodic functions (i.e. Schwartz functions) occurs when one of them is convolved in the normal way with a periodic summation of the other function.
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Compact operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset (has compact closure) of Y. Such an operator is necessarily a bounded operator, and so continuous.
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Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
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Cyclic group
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Electronics
Electronics is the discipline dealing with the development and application of devices and systems involving the flow of electrons in a vacuum, in gaseous media, and in semiconductors.
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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Fredholm kernel
In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space.
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Fredholm operator
In mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of integral equations.
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Fredholm theory
In mathematics, Fredholm theory is a theory of integral equations.
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Frequency domain
In electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Generalized function
In mathematics, generalized functions, or distributions, are objects extending the notion of functions.
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Hankel transform
In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind.
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Hartley transform
In mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions to real-valued functions.
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Hermite transform
In mathematics, Hermite transform is an integral transform named after the mathematician Charles Hermite, which uses Hermite polynomials H_n(x) as kernels of the transform.
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Hilbert transform
In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function, u(t) of a real variable and produces another function of a real variable H(u)(t).
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Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
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Integro-differential equation
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function.
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Inverse Laplace transform
In mathematics, the inverse Laplace transform of a function F(s) is the piecewise-continuous and exponentially-restricted real function f(t) which has the property: where \mathcal denotes the Laplace transform.
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Jacobi transform
In mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P_n^(x) as kernels of the transform.
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Kernel (statistics)
The term kernel is a term in statistical analysis used to refer to a window function.
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Kernel method
In machine learning, kernel methods are a class of algorithms for pattern analysis, whose best known member is the support vector machine (SVM).
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Laguerre transform
In mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials L_n^\alpha(x) as kernels of the transform.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Legendre transform
In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials P_n(x) as kernels of the transform.
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Line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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List of Fourier-related transforms
This is a list of linear transformations of functions related to Fourier analysis.
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List of mathematic operators
In mathematics, an operator or transform is a function from one space of functions to another.
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List of transforms
This is a list of transforms in mathematics.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mellin transform
In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.
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Nachbin's theorem
In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function.
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Nuclear operator
In mathematics, a nuclear operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear operators do not have a trace).
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Operator (mathematics)
In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space.
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Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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Poisson kernel
In potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disc.
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Propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum.
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Reproducing kernel Hilbert space
In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional.
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Schwartz kernel theorem
In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952.
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Sine
In mathematics, the sine is a trigonometric function of an angle.
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Sine and cosine transforms
In mathematics, the Fourier sine and cosine transforms are forms of the Fourier integral transform that do not use complex numbers.
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Stochastic discount factor
The stochastic discount factor (SDF) is a concept in financial economics and mathematical finance.
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Symbolic integration
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a differentiable function F(x) such that This is also denoted.
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Time domain
Time domain is the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Two-sided Laplace transform
In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment generating function.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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Voltage
Voltage, electric potential difference, electric pressure or electric tension (formally denoted or, but more often simply as V or U, for instance in the context of Ohm's or Kirchhoff's circuit laws) is the difference in electric potential between two points.
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Weierstrass transform
In mathematics, the Weierstrass transform of a function, named after Karl Weierstrass, is a "smoothed" version of obtained by averaging the values of, weighted with a Gaussian centered at x.
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Integral kernel, Integral operator, Integral operators, Integral transforms, Inverse kernel, Kernel (analysis), Kernel (integral equation), Kernel (integral operator), Symmetric kernel, Transform (Mathematics).
References
[1] https://en.wikipedia.org/wiki/Integral_transform
