Harmonic analysis

By Vladimir I. Clue. 2004 IEEE Electro/Information Technology Conference, 2004

1,284 citations recorded by the source corpus.

This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying. There is a connection between harmonic equations in rectangular and polar coordinate systems. The connection established here and used to create a very robust recursive algorithm for a conformal mapping calculation. There is also suggested a new ratio (and an efficient way of computing it) of two oscillative signal.

Subfields: Applied Mathematics, Mechanics of Materials, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/6ddacdbc793bafdb3ad88a38d62b2e75ff88eee0

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In Applied Mathematics

In Mechanics of Materials

In Ocean Engineering

Citations in the corpus

The weak-type (1,1) of Fourier integral operators of order –(n–1)/2 (2002, methodology): “[7]) we have the asymptotics ∫ e ′·∇ξΦ(x,ω)φ(x, ω) dω = e ′)φ(x, ω)e ′)πi/4λ−(n−1)/2|J(x, ω)| + .”
On the multilinear restriction and Kakeya conjectures (2005, background): “Hörmander conjectured that under certain natural non-degeneracy conditions on the associated phase function (see [27]), such operators would satisfy L → L estimates in agreement with the classical restriction conjecture.”
Inhomogeneous Strichartz estimates for the Schrödinger equation (2006, positive): “j!Γ ( n−1 2 −j ) and Γ denotes the Gamma function (see [10]).”
Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials (2007, background): “Knowing that w−1 ∈ A2, we see that the Riesz operators Rj = i−1 j D are bounded on the space L2 w−1 dx by standard results (see e.g., the corollary to Theorem 2, §V.4.2 of Stein, 1993).”