Improved spectral cluster bounds for orthonormal systems

References

[1] V. G. Avakumović, Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten, Math. Z. 65 (1956), 327–344. 10.1007/BF01473886Suche in Google Scholar

[2] N. Bez, S. Lee and S. Nakamura, Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates, Forum Math. Sigma 9 (2021), Paper No. e1. 10.1017/fms.2020.64Suche in Google Scholar

[3] M. D. Blair, X. Huang, Y. Sire and C. D. Sogge, Uniform Sobolev estimates on compact manifolds involving singular potentials, Rev. Mat. Iberoam. 38 (2022), no. 4, 1239–1286. 10.4171/rmi/1300Suche in Google Scholar

[4] M. D. Blair, X. Huang and C. D. Sogge, Improved spectral projection estimates, preprint (2022), https://arxiv.org/abs/2211.17266. Suche in Google Scholar

[5] M. D. Blair and C. D. Sogge, Logarithmic improvements in L p bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature, Invent. Math. 217 (2019), no. 2, 703–748. 10.1007/s00222-019-00873-6Suche in Google Scholar

[6] J. Bourgain and C. Demeter, The proof of the l 2 decoupling conjecture, Ann. of Math. (2) 182 (2015), no. 1, 351–389. 10.4007/annals.2015.182.1.9Suche in Google Scholar

[7] J. Bourgain, P. Shao, C. D. Sogge and X. Yao, On L p -resolvent estimates and the density of eigenvalues for compact Riemannian manifolds, Comm. Math. Phys. 333 (2015), no. 3, 1483–1527. 10.1007/s00220-014-2077-ySuche in Google Scholar

[8] M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992. 10.1007/978-1-4757-2201-7Suche in Google Scholar

[9] R. L. Frank, Eigenvalue bounds for Schrödinger operators with complex potentials. III, Trans. Amer. Math. Soc. 370 (2018), no. 1, 219–240. 10.1090/tran/6936Suche in Google Scholar

[10] R. L. Frank, M. Lewin, E. H. Lieb and R. Seiringer, Strichartz inequality for orthonormal functions, J. Eur. Math. Soc. (JEMS) 16 (2014), no. 7, 1507–1526. 10.4171/jems/467Suche in Google Scholar

[11] R. L. Frank and J. Sabin, Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates, Amer. J. Math. 139 (2017), no. 6, 1649–1691. 10.1353/ajm.2017.0041Suche in Google Scholar

[12] R. L. Frank and J. Sabin, Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces, Adv. Math. 317 (2017), 157–192. 10.1016/j.aim.2017.06.023Suche in Google Scholar

[13] P. Germain and S. L. Rydin Myerson, Bounds for spectral projectors on tori, Forum Math. Sigma 10 (2022), Paper No. e24. 10.1017/fms.2022.18Suche in Google Scholar

[14] J. Hickman, Uniform L p resolvent estimates on the torus, Math. Res. Rep. 1 (2020), 31–45. 10.5802/mrr.1Suche in Google Scholar

[15] E. Hlawka, Über Integrale auf konvexen Körpern. I, Monatsh. Math. 54 (1950), 1–36. 10.1007/BF01304101Suche in Google Scholar

[16] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. 10.1007/BF02391913Suche in Google Scholar

[17] X. Huang, Y. Sire and C. Zhang, Spectral cluster estimates for Schrödinger operators of relativistic type, J. Math. Pures Appl. (9) 155 (2021), 32–61. 10.1016/j.matpur.2021.08.004Suche in Google Scholar

[18] B. M. Levitan, On the asymptotic behavior of the spectral function of a self-adjoint differential equation of the second order, Izv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 325–352. Suche in Google Scholar

[19] E. H. Lieb and W. E. Thirring, Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett. 35 (1975), no. 11, 687–689. 10.1103/PhysRevLett.35.687Suche in Google Scholar

[20] S. S. Mondal and M. Song, Orthonormal strichartz inequalities for the ( k , a ) -generalized laguerre operator and Dunkl operator, preprint (2022), https://arxiv.org/abs/2208.12015. Suche in Google Scholar

[21] W. Müller, Lattice points in large convex bodies, Monatsh. Math. 128 (1999), no. 4, 315–330. 10.1007/s006050050066Suche in Google Scholar

[22] S. Nakamura, The orthonormal Strichartz inequality on torus, Trans. Amer. Math. Soc. 373 (2020), no. 2, 1455–1476. 10.1090/tran/7982Suche in Google Scholar

[23] T. Ren, Y. Xi and C. Zhang, An endpoint version of uniform Sobolev inequalities, Forum Math. 30 (2018), no. 5, 1279–1289. 10.1515/forum-2018-0042Suche in Google Scholar

[24] B. Simon, Trace Ideals and Their Applications, Math. Surveys Monogr. 120, American Mathematical Society, Providence, 2005. Suche in Google Scholar

[25] C. D. Sogge, Concerning the L p norm of spectral clusters for second-order elliptic operators on compact manifolds, J. Funct. Anal. 77 (1988), no. 1, 123–138. 10.1016/0022-1236(88)90081-XSuche in Google Scholar

[26] C. D. Sogge, Hangzhou Lectures on Eigenfunctions of the Laplacian, Ann. of Math. Stud. 188, Princeton University, Princeton, 2014. 10.1515/9781400850549Suche in Google Scholar

[27] C. D. Sogge, Fourier Integrals in Classical Analysis, 2nd ed., Cambridge Tracts in Math. 210, Cambridge University, Cambridge, 2017. 10.1017/9781316341186Suche in Google Scholar