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59 relations: Abelian group, Ancient Greek, Bessel function, Convergence of Fourier series, Data collection, Differential equation, Dimension, Distribution (mathematics), Domain (mathematical analysis), Eigenvalues and eigenvectors, Elias M. Stein, Fourier analysis, Fourier series, Fourier transform, Function (mathematics), Functional analysis, George Mackey, Graph (discrete mathematics), Group (mathematics), Group representation, Guido Weiss, Hardy space, Harmonic, Harmonic (mathematics), Harmonic series (music), Hearing the shape of a drum, Hilbert space, Laplace operator, Lie group, Locally compact group, Manifold, Mathematical analysis, Mathematics, Multiple (mathematics), Neuroscience, Noncommutative harmonic analysis, Number theory, Online Etymology Dictionary, Paley–Wiener theorem, Peter–Weyl theorem, Plancherel theorem, Pontryagin duality, Princeton University Press, Quantum mechanics, Representation theory, Signal processing, Special linear group, Spectral density estimation, Spherical harmonics, String (music), ..., Superposition principle, Support (mathematics), System of equations, Terence Tao, Tide, Topological group, Uncertainty principle, Wave, Yitzhak Katznelson. Expand index (9 more) »
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
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Ancient Greek
The Ancient Greek language includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD.
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Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
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Convergence of Fourier series
In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics.
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Data collection
Data collection is the process of gathering and measuring information on targeted variables in an established systematic fashion, which then enables one to answer relevant questions and evaluate outcomes.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Domain (mathematical analysis)
In mathematical analysis, a domain is any connected open subset of a finite-dimensional vector space.
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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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Elias M. Stein
Elias Menachem Stein (born January 13, 1931) is a mathematician.
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Fourier analysis
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.
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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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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
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George Mackey
George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.
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Guido Weiss
Guido L. Weiss (born 29 December 1928 in Trieste) is an American mathematician, working in analysis, especially Fourier analysis and harmonic analysis.
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Hardy space
In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane.
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Harmonic
A harmonic is any member of the harmonic series, a divergent infinite series.
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Harmonic (mathematics)
In mathematics, a number of concepts employ the word harmonic.
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Harmonic series (music)
A harmonic series is the sequence of sounds—pure tones, represented by sinusoidal waves—in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency.
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Hearing the shape of a drum
To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Locally compact group
In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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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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Multiple (mathematics)
In science, a multiple is the product of any quantity and an integer.
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Neuroscience
Neuroscience (or neurobiology) is the scientific study of the nervous system.
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Noncommutative harmonic analysis
In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups that are not commutative.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Online Etymology Dictionary
The Online Etymology Dictionary is a free online dictionary written and compiled by Douglas Harper that describes the origins of English-language words.
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Paley–Wiener theorem
In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform.
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Peter–Weyl theorem
In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian.
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Plancherel theorem
In mathematics, the Plancherel theorem is a result in harmonic analysis, proven by Michel Plancherel in 1910.
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Pontryagin duality
In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact abelian groups, such as \R, the circle, or finite cyclic groups.
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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
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Signal processing
Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.
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Special linear group
In mathematics, the special linear group of degree n over a field F is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.
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Spectral density estimation
In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal.
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Spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere.
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String (music)
A string is the vibrating element that produces sound in string instruments such as the guitar, harp, piano (piano wire), and members of the violin family.
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Superposition principle
In physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.
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Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
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System of equations
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
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Terence Tao
Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics.
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Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun and the rotation of Earth.
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Topological group
In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.
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Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.
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Wave
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport.
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Yitzhak Katznelson
Yitzhak Katznelson (יצחק כצנלסון; born 1934) is an Israeli mathematician.
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Abstract harmonic analysis, Fourier theory, Harmonic Analysis, Harmonic analysis (mathematics), Harmonics Theory.
References
[1] https://en.wikipedia.org/wiki/Harmonic_analysis
