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Fourier transform and Modular form

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Fourier transform and Modular form

Fourier transform vs. Modular form

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. In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.

Similarities between Fourier transform and Modular form

Fourier transform and Modular form have 21 things in common (in Unionpedia): Absolute convergence, Absolute value, Analytic function, Automorphic form, Compact space, Complex analysis, Complex number, Eigenfunction, Fourier series, Haar measure, Hausdorff space, Holomorphic function, If and only if, Imaginary unit, Lie group, Number theory, Periodic function, Princeton University Press, Representation theory, Springer Science+Business Media, Theta function.

Absolute convergence

In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.

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Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

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Automorphic form

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group.

Automorphic form and Fourier transform · Automorphic form and Modular form · See more »

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Eigenfunction

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue.

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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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Haar measure

In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups.

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Hausdorff space

In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.

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Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

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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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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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Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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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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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

Fourier transform and Springer Science+Business Media · Modular form and Springer Science+Business Media · See more »

Theta function

In mathematics, theta functions are special functions of several complex variables.

Fourier transform and Theta function · Modular form and Theta function · See more »

The list above answers the following questions

Fourier transform and Modular form Comparison

Fourier transform has 248 relations, while Modular form has 103. As they have in common 21, the Jaccard index is 5.98% = 21 / (248 + 103).

References

This article shows the relationship between Fourier transform and Modular form. To access each article from which the information was extracted, please visit:

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