Mock Fourier series and transforms associated with certain Cantor measures
By Robert S. Strichartz. 2000
274 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/05a411e5d14567b9a0617d88ef7fe57e84195b20
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Spectral measures generated by arbitrary and random convolutions (2015, background): “is easy to show that the measure has an infinite mutually orthogonal set (1.3) Λ = L 1+ RTL2 + ... + (RT RT 2 ...R T n− )Ln + ... The spectral property of these measures was first studied by Strichartz [Str00], in which the sequence {(Ri,Bi)} was called a compatible tower, and it has received a lot of”
- Fourier frequencies in affine iterated function systems (2006, result): “We will prove in Theorem 3.8 that the conjecture is true under some extra analytical assumptions, thus extending the known results from [JoPe98, Str00 , LaWa02, DuJo05, LaWa06].”
- A class of Gaussian processes with fractional spectral measures (2010, background): “The Fourier expansion in L2(dσ) for fractal measures σ differs from standard Fourier series (for periodic functions) in that the fractal Fourier expansion is local, much like wavelet expansions; see [37] for details.”
- Non-spectral problem for a class of planar self-affine measures (2008, background): “The spectral self-affine measure problem at the present day consists in determining conditions under which μM,D is a spectral measure, and has been studied in the papers [2–6,18,23,25,27,28,32] (see also [33,34] for the main goal).”
- Weak convergence and spectrality of infinite convolutions (2022, methodology): “[51] R. Strichartz, Convergence of mock Fourier series, J. Anal.”
- Spectral property of the Bernoulli convolutions (2008, unknown): “MSC: primary 42C05, 42A65; secondary 28A78, 28A80 Keywords: Bernoulli convolution; Minimal polynomial; Orthogonality; Spectral set; Self-similarity”
- On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem (2019, background): “[39] R. S. Strichartz, Convergence of mock Fourier series, J. Anal.”
- Combining Riesz bases (2012, background): “on is that orthogonality is too strong a requirement, it requires that each couple of exponentials have their difference in the zero set of c 1 S (a Bessel function, in the case of the ball). See also [6, 8, 28, 14, 27]. A similar statement holds for some simply constructed subsets of R, even the uni”
- Some properties of spectral measures (2006, unknown): “Interestingly, there is even evidence showing a strong connection between tiling and spectral measures, see [LabWa02] and Strichartz [ Str00 ].”
- When does a Bernoulli convolution admit a spectrum (2012, background): “It is the Bernoulli convolution μρ whose contraction rate ρ is the reciprocal of an even integer [15,29]; see [2,3,5–7,14,28,30] and references therein for recent advances on singular spectral measures.”
- Wavelets on Fractals (2003, background): “There is already a considerable body of work on harmonic analysis on fractals, see for example [22], [11], [10], [23], and [16].”