Characterizations of self-adjointness, normality of pseudo-differential operators on homogeneous space of compact groups

References

• Carey A, Ellwood D, Paycha S, et al. Motives, quantum field theory, and pseudo-differential operators. Clay Math Proc. 2010;12(1):37–72.
   Google Scholar
• Hörmander L. The analysis of linear partial differential operators. III. Berlin: Springer-Verlag; 1985.
   Google Scholar
• Kohn JJ, Nirenberg L. An algebra of pseudo-differential operators. Comm Pure Appl Math. 1965;18;269–305.
   Web of Science ®Google Scholar
• Cardona D, Kumar V. Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on Zn and the torus Tn. J Fourier Anal Appl. 2019;25(6):2973–3017.
   Web of Science ®Google Scholar
• Cardona D. On the nuclear trace of Fourier integral operators. Rev Integr Temas Mat. 2019;37(2):219–249.
   Google Scholar
• Cardona D, Kumar V. Multilinear analysis for discrete and periodic pseudo-differential operators in Lp spaces. Rev Integr Temas Mat. 2018;36(2):151–164.
   Google Scholar
• Dasgupta A, Wong MW. Pseudo-differential operators on the affine group, Pseudo-differential operators: groups, geometry and applications, Trends Math., Birkhäuser/Springer, Cham; 2017. p. 1–14.
   Google Scholar
• Dasgupta A, Kumar V. Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group, (2019) submitted (2019). https://arxiv.org/abs/1902.09869.
   Google Scholar
• Delgado J, Ruzhansky M. Schatten classes and traces on compact groups. Math Res Lett. 2017;24(4):979–1003.
   Web of Science ®Google Scholar
• Ghaemi MB, Jamalpourbirgani M, Wong MW. Characterizations, adjoints and products of nuclear pseudo-differential operators on compact and Hausdorff groups. U P B Sci Bull Ser A. 2017;79(4):207–220.
   Google Scholar
• Kumar V. Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups. Forum Math. 2019;31(2):275–282.
   Web of Science ®Google Scholar
• Kumar V, Mondal SS. Nuclearity of operators related to finite measure spaces. J Pseudo-Differ Oper Appl. 2020;11(3):1031–1058. https://doi.org/https://doi.org/10.1007/s11868-020-00353-z.
   Web of Science ®Google Scholar
• Molahajloo S, Pirhayati M. Traces of pseudo-differential operators on compact and Hausdorff groups. J Pseudo-Differ Oper Appl. 2013;4(3):361–369.
   Web of Science ®Google Scholar
• Molahajloo S, Wong KL. Pseudo-differential operators on finite abelian groups. J Pseudo-Differ Oper Appl. 2015;6:1–9.
   Web of Science ®Google Scholar
• Ruzhansky M, Turunen V. Pseudo-differential operators and symmetries: background analysis and advanced topics. Basel: Birkhäuser-Verlag; 2010.
   Google Scholar
• Wong MW. An introduction to pseudo-differential operators. 3rd edn. Singapore/Teaneck: World Scientific; 2014.
   Google Scholar
• Ruzhansky M, Turunen V. Global quantization of pseudo-differential operators on compact lie groups SU(2), 3-Sphere, and homogeneous spaces. Int Math Res Not IMRN. 2013;(11):2439–2496.
   Google Scholar
• Delgado J, Ruzhansky M. Lp-bounds for pseudo-differential operators on compact Lie groups. J Inst Math Jussieu. 2019;18(3):531–559.
   Web of Science ®Google Scholar
• Ghaemi MB, Jamalpourbirgani M. Lp -boundedness compactness of pseudo-differential operators on compact Lie groups. J Pseudo-Differ Oper Appl. 2017;8:1–11.
   Web of Science ®Google Scholar
• Ghaemi MB, Jamalpourbirgani M, Nabizadeh Morsalfard E. A study on pseudo-differential operators on S1 and Z. J Pseudo-Differ Oper Appl. 2016;7:237–247.
   Web of Science ®Google Scholar
• Jamalpourbirgani M, Wong MW. Characterizations of self-adjointness, normality, invertibility, and unitarity of pseudo-differential operators on compact and Hausdorff groups. In Analysis of Pseudo-differential operators, Birkhäuser (2019).
   Google Scholar
• Molahajloo S. A characterization of compact pseudo-differential operators on S1, in Pseudo-Differential Operators: Analysis, Applications and Computations, Birkhäuser; 2011. p. 25–31.
   Google Scholar
• Wong MW. Wavelet transforms and localization operators. Basel: Birkhäuser; 2002.
   Google Scholar
• Kisil V. Relative convolutions I. Properties and applications. Adv Math. 1999;147(1):35–73.
   Web of Science ®Google Scholar
• Kisil V. Erlangen program at large: an overview, In Advances in applied analysis, Trends Math., Birkhäuser/Springer (2012).
   Google Scholar
• Kisil V. Geometry of M$\ddot{\mathrm{o}}$bius transformations. elliptic parabolic and hyperbolic actions of $S{L}_2(\mathbb{R})$. London: Imperial College Press; 2012.
   Google Scholar
• Kisil V. Calculus of operators: covariant transform and relative convolutions. Banach J Math Anal. 2014;8(2):156–184.
   Web of Science ®Google Scholar
• Ghani Farashahi A. Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups. Groups Geom Dyn. 2017;11(4):1437–1467.
   Web of Science ®Google Scholar
• Kumar V, Mondal SS. Schatten class and nuclear pseudo-differential operators on homogeneous spaces of compact groups. 2019;1–24. https://arxiv.org/abs/1911.10554.
   Google Scholar
• Dasgupta A, Ruzhansky M. Gevrey functions and ultra distributions on compact Lie groups and homogeneous spaces. Bull Sci Math. 2014;138(6):756–782.
   Web of Science ®Google Scholar
• Delgado J, Ruzhansky M. Fourier multipliers symbols and nuclearity on compact manifolds. J Anal Math. 2018;135:757–800.
   Web of Science ®Google Scholar
• Nursultanov E, Ruzhansky M, Tikhonov S. Nikolskii inequality and Besov Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds. Ann Sc Norm Super Pisa Cl Sci. 2016;16:981–1017.
   Google Scholar
• Limaye BV. Functional analysis. Second edition.New Delhi: New age international LTD; 1996.
   Google Scholar