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Isomorphism between one-dimensional and multidimensional finite difference operators
On optimal autocorrelation inequalities on the real line
1. | Department of Mathematics, University of California, Los Angeles, Portola Plaza 520, Los Angeles, California, 90095, USA |
2. | Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil |
We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work [
References:
[1] |
R.C. Barnard and S. Steinerberger,
Three convolution inequalities on the real line with connection to additive combinatorics, J. Number Theory, 207 (2020), 42-55.
doi: 10.1016/j.jnt.2019.07.001. |
[2] |
W. Beckner,
Inequalities in Fourier analysis, Ann. Math., 102 (1975), 159-182.
doi: 10.2307/1970980. |
[3] |
J. Bourgain, L. Clozel and J.P. Kahane, Principe d'Heisenberg et fonctions positives, Annales de l'institut Fourier, 60 (2010), 1215-1232. Google Scholar |
[4] |
J. Cilleruelo, I. Ruzsa and C. Trujillo,
Upper and lower bounds for finite $Bh[g]$ sequences, J. Number Theory, 97 (2002), 26-34.
doi: 10.1006/jnth.2001.2767. |
[5] |
J. Cilleruelo, I. Ruzsa and C. Vinuesa, Generalized Sidon sets, Adv. Math., 225 (2010), 2786 –2807.
doi: 10.1016/j.aim.2010.05.010. |
[6] |
A. Cloninger and S. Steinerberger,
On suprema of autoconvolutions with an application to Sidon sets, P. Am. Math. Soc., 145 (2017), 3191-3200.
doi: 10.1090/proc/13690. |
[7] |
H. Cohn and F. Gonçalves,
An optimal uncertainty principle in twelve dimensions via modular forms, Inventionnes Mathematicae, 217 (2019), 799-831.
doi: 10.1007/s00222-019-00875-4. |
[8] |
S. Fish, D. King and S. J. Miller, Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics, arXiv: 2001.02326. Google Scholar |
[9] |
G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, 2016.
![]() |
[10] |
F. Gonçalves, D. Oliveira e Silva and J. P. G. Ramos, New sign uncertainty principles, Preprint, 2020. Google Scholar |
[11] |
F. Gonçalves, D. Oliveira e Silva and J. P. G. Ramos, On regularity and mass concentration phenomena for the sign uncertainty principle, Preprint, 2020. Google Scholar |
[12] |
F. Gonçalves, D. Oliveira e Silva and S. Steinerberger,
Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots, J. Math. Anal. Appl., 451 (2017), 678-711.
doi: 10.1016/j.jmaa.2017.02.030. |
[13] |
B. Green,
The number of squares and $Bh[g]$ sets, Acta Arith., 100 (2001), 365-390.
doi: 10.4064/aa100-4-6. |
[14] |
G. Martin and K. O'Bryant,
Constructions of generalized Sidon sets, J. Comb. Theory A, 113 (2006), 591-607.
doi: 10.1016/j.jcta.2005.04.011. |
[15] |
G. Martin and K. O'Bryant,
The symmetric subset problem in continuous Ramsey theory, Exp. Math., 16 (2007), 145-166.
|
[16] |
M. Matolcsi and C. Vinuesa,
Improved bounds on the supremum of autoconvolutions, J. Math. Anal. Appl., 372 (2010), 439-447.
doi: 10.1016/j.jmaa.2010.07.030. |
[17] |
G. Yu,
An upper bound for $B2[g]$ sets, J. Number Theory, 122 (2007), 211-220.
doi: 10.1016/j.jnt.2006.04.008. |
show all references
References:
[1] |
R.C. Barnard and S. Steinerberger,
Three convolution inequalities on the real line with connection to additive combinatorics, J. Number Theory, 207 (2020), 42-55.
doi: 10.1016/j.jnt.2019.07.001. |
[2] |
W. Beckner,
Inequalities in Fourier analysis, Ann. Math., 102 (1975), 159-182.
doi: 10.2307/1970980. |
[3] |
J. Bourgain, L. Clozel and J.P. Kahane, Principe d'Heisenberg et fonctions positives, Annales de l'institut Fourier, 60 (2010), 1215-1232. Google Scholar |
[4] |
J. Cilleruelo, I. Ruzsa and C. Trujillo,
Upper and lower bounds for finite $Bh[g]$ sequences, J. Number Theory, 97 (2002), 26-34.
doi: 10.1006/jnth.2001.2767. |
[5] |
J. Cilleruelo, I. Ruzsa and C. Vinuesa, Generalized Sidon sets, Adv. Math., 225 (2010), 2786 –2807.
doi: 10.1016/j.aim.2010.05.010. |
[6] |
A. Cloninger and S. Steinerberger,
On suprema of autoconvolutions with an application to Sidon sets, P. Am. Math. Soc., 145 (2017), 3191-3200.
doi: 10.1090/proc/13690. |
[7] |
H. Cohn and F. Gonçalves,
An optimal uncertainty principle in twelve dimensions via modular forms, Inventionnes Mathematicae, 217 (2019), 799-831.
doi: 10.1007/s00222-019-00875-4. |
[8] |
S. Fish, D. King and S. J. Miller, Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics, arXiv: 2001.02326. Google Scholar |
[9] |
G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, 2016.
![]() |
[10] |
F. Gonçalves, D. Oliveira e Silva and J. P. G. Ramos, New sign uncertainty principles, Preprint, 2020. Google Scholar |
[11] |
F. Gonçalves, D. Oliveira e Silva and J. P. G. Ramos, On regularity and mass concentration phenomena for the sign uncertainty principle, Preprint, 2020. Google Scholar |
[12] |
F. Gonçalves, D. Oliveira e Silva and S. Steinerberger,
Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots, J. Math. Anal. Appl., 451 (2017), 678-711.
doi: 10.1016/j.jmaa.2017.02.030. |
[13] |
B. Green,
The number of squares and $Bh[g]$ sets, Acta Arith., 100 (2001), 365-390.
doi: 10.4064/aa100-4-6. |
[14] |
G. Martin and K. O'Bryant,
Constructions of generalized Sidon sets, J. Comb. Theory A, 113 (2006), 591-607.
doi: 10.1016/j.jcta.2005.04.011. |
[15] |
G. Martin and K. O'Bryant,
The symmetric subset problem in continuous Ramsey theory, Exp. Math., 16 (2007), 145-166.
|
[16] |
M. Matolcsi and C. Vinuesa,
Improved bounds on the supremum of autoconvolutions, J. Math. Anal. Appl., 372 (2010), 439-447.
doi: 10.1016/j.jmaa.2010.07.030. |
[17] |
G. Yu,
An upper bound for $B2[g]$ sets, J. Number Theory, 122 (2007), 211-220.
doi: 10.1016/j.jnt.2006.04.008. |
[1] |
Andrea Cianchi, Adele Ferone. Improving sharp Sobolev type inequalities by optimal remainder gradient norms. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1363-1386. doi: 10.3934/cpaa.2012.11.1363 |
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