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Average error for spectral asymptotics on surfaces
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Average number of lattice points in a disk
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2. | Mathematics Department, Malott Hall, Cornell Univeristy, Ithaca, NY 14853, United States |
References:
[1] |
M. Begué, T. Kalloniatis and R. Strichartz, Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet, Fractals, 21 (2013), 13500023 (32 pages).
doi: 10.1142/S0218348X13500023. |
[2] |
P. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math J., 67, 461-481.
doi: 10.1215/S0012-7094-92-06718-4. |
[3] |
P. Bleher, Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems, Duke Math J., 70, 655-682.
doi: 10.1215/S0012-7094-93-07015-9. |
[4] |
M. Huxley, The mean lattice discrepancy, Proc. Edinburg Math. Soc., 38 (1995), 523-531.
doi: 10.1017/S0013091500019313. |
[5] |
H. Iwaniec and E. Kowalski, Analytic Number Theory, AMS Colloq. Publ. vol 53, 2004. |
[6] |
S. Jayakar and R. Strichartz, Average number of lattice points in a disk, http://www.math.cornell.edu/ sujay/lattice, 2012. |
[7] |
N. Lebedev, Special Functions and Their Applications, Dover Publications, New York, 1965. |
[8] |
W. Müller, On the average order of the lattice rest of a convex body, Acta Arith., 80 (1997), 89-100. |
[9] |
C. Sogge, Hangzhou Lectures on Eigenfunctions of the Laplacian, Princeton Univ. Press, Princeton, 2014.
doi: 10.1515/9781400850549. |
[10] |
E. Stein and R. Shakarchi, Functional Analysis, Princeton Univ. Press, 2011. |
[11] |
R. Strichartz, Average error for spectral asymptotics on surfaces, Comm. Pure Appl. Analysis, 15 (2016), 9-39. |
show all references
References:
[1] |
M. Begué, T. Kalloniatis and R. Strichartz, Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet, Fractals, 21 (2013), 13500023 (32 pages).
doi: 10.1142/S0218348X13500023. |
[2] |
P. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math J., 67, 461-481.
doi: 10.1215/S0012-7094-92-06718-4. |
[3] |
P. Bleher, Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems, Duke Math J., 70, 655-682.
doi: 10.1215/S0012-7094-93-07015-9. |
[4] |
M. Huxley, The mean lattice discrepancy, Proc. Edinburg Math. Soc., 38 (1995), 523-531.
doi: 10.1017/S0013091500019313. |
[5] |
H. Iwaniec and E. Kowalski, Analytic Number Theory, AMS Colloq. Publ. vol 53, 2004. |
[6] |
S. Jayakar and R. Strichartz, Average number of lattice points in a disk, http://www.math.cornell.edu/ sujay/lattice, 2012. |
[7] |
N. Lebedev, Special Functions and Their Applications, Dover Publications, New York, 1965. |
[8] |
W. Müller, On the average order of the lattice rest of a convex body, Acta Arith., 80 (1997), 89-100. |
[9] |
C. Sogge, Hangzhou Lectures on Eigenfunctions of the Laplacian, Princeton Univ. Press, Princeton, 2014.
doi: 10.1515/9781400850549. |
[10] |
E. Stein and R. Shakarchi, Functional Analysis, Princeton Univ. Press, 2011. |
[11] |
R. Strichartz, Average error for spectral asymptotics on surfaces, Comm. Pure Appl. Analysis, 15 (2016), 9-39. |
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