Results 1 to 10 of about 752,727 (270)

Quantization of pseudo-differential operators on the torus [PDF]

, 2008
Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts.
Ruzhansky, Michael, Turunen, Ville
core   +3 more sources

Vector valued formal Fourier-Jacobi series [PDF]

, 2014
H. Aoki showed that any symmetric formal Fourier-Jacobi series for the symplectic group Sp_2(Z) is the Fourier-Jacobi expansion of a holomorphic Siegel modular form.
Bruinier, Jan Hendrik
core   +1 more source

Fourier Series Formalization in ACL2(r) [PDF]

, 2015
We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis.
Chau, Cuong K., Hunt Jr., Warren A., Kaufmann, Matt   +2 more
core   +3 more sources

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups [PDF]

, 2010
We define lacunary Fourier series on a compact connected semisimple Lie group $G$. If $f \in L^1(G)$ has lacunary Fourier series, and vanishes on a non empty open set, then we prove that $f$ vanishes identically.
Narayanan, E K, Sitaram, A
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Fractional Derivative as Fractional Power of Derivative [PDF]

, 2007
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator.
Berezin F. A., Berezin F. A., Brichkov Yu. A., Caputo M., Dalechky Yu. L., Hadid S. B., Karasev M. V., Korabel N., Krasnolelsky M. A., Krasnolelsky M. A., Krein S. G., Krein S. G., Le Mehaute A., Luke Y., Maslov V. P., Momani S., Oldham K. B., Samko S. G., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., VASILY E. TARASOV, Zaslavsky G. M.   +25 more
core   +1 more source

On the order of summability of the Fourier inversion formula [PDF]

, 2010
In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related.
A. Denjoy, A. Zygmund, E. C. Titchmarsh, E. Seneta, E. W. Hobson, F. J. González Vieli, F. Lukács, F. Móricz, F. Móricz, G. H. Hardy, G. H. Hardy, G. H. Hardy, G. H. Hardy, G. H. Hardy, G. Walter, G. Walter, G. Walter, H. Bremermann, J. Campos Ferreira, J. Marcinkiewicz, J. Vindas, J. Vindas, J. Vindas, J. Vindas, J. Vindas, J. Vindas, J. Vindas, Jasson Vindas, L. Fejér, L. Schwartz, M. Plancherel, R. A. Gordon, R. Estrada, R. Estrada, R. Estrada, R. Estrada, R. Estrada, Ricardo Estrada, S. Bochner, S. Bochner, S. Pilipović, S. Łojasiewicz, T. H. Gronwall, V. S. Vladimirov, V. S. Vladimirov   +44 more
core   +3 more sources

Fast Algorithms for the computation of Fourier Extensions of arbitrary length [PDF]

, 2015
Fourier series of smooth, non-periodic functions on $[-1,1]$ are known to exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of overcoming these problems is by using a Fourier series on a larger domain, say $[-T,T]$ with $T>1$, a
Daan Huybrechs, Daan Huybrechs, Roel Matthysen, Roel Matthysen   +3 more
core   +3 more sources

BMO-estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series

, 2013
It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier ...
Goginava, U., Gogoladze, L., Karagulyan, G.   +2 more
core   +1 more source

Abel Summation of Ramanujan-Fourier Series [PDF]

, 2015
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions.
Washburn, John
core  

On uniform convergence of Fourier series

, 2012
We consider the space $U(\mathbb T)$ of all continuous functions on the circle $\mathbb T$ with uniformly convergent Fourier series. We show that if $\varphi: \mathbb T\rightarrow\mathbb T$ is a continuous piecewise linear but not linear map, then $\|e ...
A. Beurling, A.M. Olevskii, J.-P. Kahane, J.-P. Kahane, V. V. Lebedev, V. V. Lebedev   +5 more
core   +1 more source