Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic ...

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### Can a positive polynomial on sphere be represented as the sum of squares of spherical harmonics

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### Regarding convolution of fejer kernel with a lipschitz function

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### Is Serre duality related to Pontryagin duality?

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### gaussian upper bound on spherical heat kernel

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### Convolution theorem on a non-abelian Lie group

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### Multiplicities in Plancherel theorem for SL2(R)

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### Solvability of Neumann boundary problems with singular boundary data $g \in (H^{1})^{*}$

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### Is the Gelfand transform strictly continuous?

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### Uniqueness of solution depending on constant?

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### Number theory on Banach space $L^2(\mathbb R)$ meets linear independence?

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### Relation between Lie group characters and spherical functions on symmetric spaces

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### About Vitali covering theorem

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### Invariant subspace in infinite dimensions

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### $L^2$ function in Schwartz space?

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### Characterizing pseudo-differential operators as a subalgebra of continuous endomorphisms of tempered distributions

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### Decay of Fourier coefficients for Hölder functions on compact Lie groups

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### A combinatorial proof of the Harrow--Kolla--Schulman theorem

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### Infinitely many independent functions that are only frequency localized?

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### Is there a physical/geometric proof for L^2 boundedness of Bourgain's maximal function along the squares?

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### What are the LCA groups that are the Pontryagin dual of a locally profinite abelian group?

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### About understanding manifold structure on WAP compactification of $\Bbb{C} \rtimes \Bbb{T}$

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### Spectral theory for Fuchsian groups of the first kind

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### Partial derivatives of spherical harmonics

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### Are the Prolate Spheroidal Wave Functions absolutely integrable?

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### Hölder-Zygmund spaces of negative order

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### Is it possible to find an atlas for the set: $\{F:FE = I, E \text{ is a frame for } \mathbb{R}^n\}$

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### Is Weierstrass function nowhere pointwise Lipschitz?

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### A specific Schwartz function $f$ on $\mathbb C^2$

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### $L^p$ estimates and functions with positive Fourier transform

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### Determinant of a matrix involving the Prolate Spheroidal Wave Functions

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### Differentiability of the logarithmic potential

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### Sharp assumption on domain for elliptic boundary regularity

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### Harmonic analysis on constant curvature hyperbolic spaces of arbitrary dimension

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### global estimate for biharmonic function

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### On the bound of the Stein-Wainger oscillatory integral

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### Is the maximal function bounded on the Besov space?

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### Decay of bandlimited function

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### Differentiation on $[0,1]$

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### Square-integrability of non-holomorphic Poincare series

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### Proof of $L^1(\mathbb{R}) \ast f \neq L^1(\mathbb{R})$

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### Are there any non-trivial convergent sequences in the maximal ideal space of the measure algebra?

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### Does Novikov condition imply BMO martingale?

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### When is a minimal immersion holomorphic?

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### Solving classical parabolic equation by using Littlewood-Paley theory

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### Is the product of two Sobolev functions in L^p?

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### What is the intuition behind Almgren's frequency function?

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### Inclusion of Hardy spaces

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### Bound of analytic torsion for a line bundle

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### Plancharel-Pólya inequality for functions of exponential type

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