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21 relations: Almost everywhere, Banach space, Complex conjugate, Eigenfunction, Fourier series, Function space, Hilbert space, Inner product space, Interpolation, Interval (mathematics), Legendre polynomials, Mathematical analysis, Orthogonal functions, Orthogonality, Orthonormal basis, Real line, Square-integrable function, Sturm–Liouville theory, Topological vector space, Vector space, Weight function.
Almost everywhere
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.
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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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Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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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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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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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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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Legendre polynomials
In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.
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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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Orthogonal functions
In mathematics, orthogonal functions belong to a function space which is a vector space that has a bilinear form.
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Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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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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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
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Sturm–Liouville theory
In mathematics and its applications, a classical Sturm–Liouville theory, named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882), is the theory of a real second-order linear differential equation of the form where y is a function of the free variable x. Here the functions p(x), q(x), and w(x) > 0 are specified at the outset.
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Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Weight function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.
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References
[1] https://en.wikipedia.org/wiki/Generalized_Fourier_series
