Abstract
In this paper we study multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of r-nuclear operators on Lebesgue spaces. We also study the nuclear trace and the spectral trace of these operators.
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Bagchi, S., Thangavelu, S.: On Hermite pseudo-multipliers. J. Funct. Anal. 268(1), 140–170 (2015)
Cardona, D.: Nuclear pseudo-differential operators in Besov spaces on compact Lie groups; to appear in J. Fourier Anal. Appl. (2017)
Delgado, J.: A trace formula for nuclear operators on \(L^p\). In: Schulze, B.W., Wong, M.W. (Eds.), Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations, Operator Theory: Advances and Applications, vol. 205, pp. 181–193. Birkhuser, Basel (2010)
Delgado, J., Wong, M.W.: \(L^p\)-nuclear pseudo-differential operators on \({\mathbb{Z}}\) and \({\mathbb{S}}^1\). Proc. Amer. Math. Soc. 141(11), 3935–394 (2013)
Delgado, J.: The trace of nuclear operators on \(L^p(\mu )\) for \(\sigma \)-finite Borel measures on second countable spaces. Integral Equ. Oper. Theor. 68(1), 61–74 (2010)
Delgado, J.: On the \(r\)-nuclearity of some integral operators on Lebesgue spaces. Tohoku Math. J. 67(2), no. 1, 125–135 (2015)
Delgado, J., Ruzhansky, M., Wang, B.: Approximation property and nuclearity on mixed-norm \(L^p\), modulation and Wiener amalgam spaces. J. Lond. Math. Soc. 94, 391–408 (2016)
Delgado, J., Ruzhansky, M., Wang, B.: Grothendieck-Lidskii trace formula for mixed-norm \(L^p\) and variable Lebesgue spaces. to appear in J. Spectr. Theory
Delgado, J., Ruzhansky, M.: \(L^p\)-nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups., J. Math. Pures Appl. 9(102)(1), 153–172 (2014)
Delgado, J., Ruzhansky, M.: Schatten classes on compact manifolds: kernel conditions. J. Funct. Anal. 267(3), 772–798 (2014)
Delgado, J., Ruzhansky, M.: Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds. C. R. Acad. Sci. Paris. Ser. I. 352, 779–784 (2014)
Delgado, J., Ruzhansky, M.: Fourier multipliers, symbols and nuclearity on compact manifolds. arXiv:1404.6479
Delgado, J., Ruzhansky, M.: Schatten-von Neumann classes of integral operators. arXiv:1709.06446
Delgado, J., Ruzhansky, M., Tokmagambetov, N.: Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary. arXiv:1505.02261
Epperson, J.: Hermite multipliers and pseudo-multipliers. Proc. Amer. Math. Soc. 124(7), 2061–2068 (1996)
Ghaemi, M.B., Jamalpour Birgani, M., Wong, M.W.: Characterizations of nuclear pseudo-differential operators on S1 with applications to adjoints and products. J. Pseudo-Differ. Oper. Appl. 8(2), 191–201 (2017)
Grothendieck, A.: La theorie de Fredholm. Bull. Soc. Math. Fr. 84, 319–384 (1956)
Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires, Memoirs Amer. Math. Soc. 16, Providence (1955) (Thesis, Nancy, 1953)
Koch, H., Tataru, D.: \(L^p\)-eigenfunction bounds for the Hermite operator. Duke Math. J. 128, 369–392 (2005)
Prugovec̆ki, E.: Quantum mechanics in Hilbert space. 2 edn. Pure and Applied Mathematics, 92. Academic Press, Inc, New York-London (1981)
Pietsch, A.: Operator ideals. Mathematische Monographien, 16. VEB Deutscher Verlag der Wissenschaften, Berlin (1978)
Pietsch, A.: History of Banach Spaces and Linear Operators. Birkhäuser Boston Inc, Boston, MA (2007)
Reinov, O.I., Latif, Q.: Grothendieck-Lidskii theorem for subspaces of Lpspaces. Math. Nachr. 286(2–3), 279–282 (2013)
Nicola, F., Rodino, L.: Global Pseudo-differential Calculus on Euclidean Spaces. Pseudo-Differential Operators. Theory and Applications, 4. Birkhuser Verlag, Basel (2010)
Simon, B.: Distributions and their Hermite expansions. J. Math. Phys. 12, 140–148 (1971)
Stempak, K.: Multipliers for eigenfunction expansions of some Schrdinger operators. Proc. Amer. Math. Soc. 93, 477–482 (1985)
Stempak, K., Torre, J.L.: On g-functions for Hermite function expansions. Acta Math. Hung. 109, 99–125 (2005)
Stempak, K., Torre, J.L.: BMO results for operators associated to Hermite expansions. Illinois J. Math. 49, 1111–1132 (2005)
Thangavelu, S.: Lectures on Hermite and Laguerre Expansions, Math. Notes, vol. 42, Princeton University Press, Princeton (1993)
Thangavelu, S.: Hermite and special Hermite expansions revisited. Duke Math. J. 94(2), 257–278 (1998)
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Barraza, E.S., Cardona, D. (2019). On Nuclear \(L^p\)-Multipliers Associated to the Harmonic Oscillator. In: Delgado, J., Ruzhansky, M. (eds) Analysis and Partial Differential Equations: Perspectives from Developing Countries. Springer Proceedings in Mathematics & Statistics, vol 275. Springer, Cham. https://doi.org/10.1007/978-3-030-05657-5_4
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