Operators with complex Gaussian kernels: boundedness properties

Negrín, E. R.

doi:10.1090/S0002-9939-1995-1227527-5

Operators with complex Gaussian kernels: boundedness properties
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by E. R. Negrín

Proc. Amer. Math. Soc. 123 (1995), 1185-1190

DOI: https://doi.org/10.1090/S0002-9939-1995-1227527-5

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Abstract:

Boundedness properties are stated for some operators from ${L^p}(\mathbb {R})$ into ${L^q}(\mathbb {R}),1 \leq p,q \leq \infty$, with complex Gaussian kernels. Their contraction properties are also analysed.

References

John C. Baez, Irving E. Segal, and Zheng-Fang Zhou, Introduction to algebraic and constructive quantum field theory, Princeton Series in Physics, Princeton University Press, Princeton, NJ, 1992. MR 1178936, DOI 10.1515/9781400862504
Jay B. Epperson, The hypercontractive approach to exactly bounding an operator with complex Gaussian kernel, J. Funct. Anal. 87 (1989), no. 1, 1–30. MR 1025881, DOI 10.1016/0022-1236(89)90002-5
Gerald B. Folland, Harmonic analysis in phase space, Annals of Mathematics Studies, vol. 122, Princeton University Press, Princeton, NJ, 1989. MR 983366, DOI 10.1515/9781400882427
Roger Howe, The oscillator semigroup, The mathematical heritage of Hermann Weyl (Durham, NC, 1987) Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, RI, 1988, pp. 61–132. MR 974332, DOI 10.1090/pspum/048/974332
Elliott H. Lieb, Gaussian kernels have only Gaussian maximizers, Invent. Math. 102 (1990), no. 1, 179–208. MR 1069246, DOI 10.1007/BF01233426
Fred B. Weissler, Two-point inequalities, the Hermite semigroup, and the Gauss-Weierstrass semigroup, J. Functional Analysis 32 (1979), no. 1, 102–121. MR 533222, DOI 10.1016/0022-1236(79)90080-6