Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
-
Vishvesh Kumar
Abstract
Let G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space
Funding source: Council of Scientific and Industrial Research
Award Identifier / Grant number: 09/086(1204)/2014-EMR-I
Funding statement: The author wishes to thank the Council of Scientific and Industrial Research, India, for Senior Research Fellowship (09/086(1204)/2014-EMR-I).
Acknowledgements
The author expresses his deep gratitude to Prof. M. W. Wong for several insightful conversations. He thanks his supervisors Ritumoni Sarma and N. Shravan Kumar for their support and encouragement. He would also like to thank the referee for his/her valuable suggestions.
References
[1]
Z. Chen and M. W. Wong,
Traces of pseudo-differential operators on
[2] A. Dasgupta and M. W. Wong, Pseudo-differential operators on the affine group, Pseudo-Differential Operators: Groups, Geometry and Applications, Trends Math., Birkhäuser/Springer, Cham (2017), 1–14. 10.1007/978-3-319-47512-7_1Search in Google Scholar
[3] J. Delgado and M. Ruzhansky, Schatten classes and traces on compact groups, Math. Res. Lett. 24 (2017), no. 4, 979–1003. 10.4310/MRL.2017.v24.n4.a3Search in Google Scholar
[4]
J. Delgado and M. W. Wong,
[5] A. Ghaani Farashahi, Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups, Groups Geom. Dyn. 11 (2017), no. 4, 1437–1467. 10.4171/GGD/434Search in Google Scholar
[6] A. Ghaani Farashahi, Abstract Plancherel (trace) formulas over homogeneous spaces of compact groups, Canad. Math. Bull. 60 (2017), no. 1, 111–121. 10.4153/CMB-2016-037-6Search in Google Scholar
[7] A. Ghani Farashahi, Peter–Weyl theorem for homogeneous spaces of compact groups, Int. J. Anal. Appl. 13 (2017), no. 1, 22–31. Search in Google Scholar
[8] A. Ghaani Farashahi, Trigonometric polynomials over homogeneous spaces of compact groups, Adv. Oper. Theory 2 (2017), no. 1, 87–97. 10.4153/CJM-2016-043-9Search in Google Scholar
[9] M. B. Ghaemi, M. Jamalpourbirgani and M. W. Wong, Characterizations, adjoints and products of nuclear pseudo-differential operators on compact and Hausdorff groups, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 79 (2017), no. 4, 207–220. Search in Google Scholar
[10]
M. B. Ghaemi, M. Jamalpour Birgani and M. W. Wong,
Characterizations of nuclear pseudo-differential operators on
[11] L. Hörmander, The Analysis of Linear Partial Differential Operators. III, Grundlehren Math. Wiss. 274, Springer, Berlin, 1985. Search in Google Scholar
[12] A. A. Kirillov and A. D. Gvishiani, Theorems and problems of functional analysis (in Russian), 2nd ed., Nauka, Moscow, 1988. Search in Google Scholar
[13] V. V. Kisil, Relative convolutions. I. Properties and applications, Adv. Math. 147 (1999), no. 1, 35–73. 10.1006/aima.1999.1833Search in Google Scholar
[14] V. V. Kisil, Erlangen program at large: An overview, Advances in Applied Analysis, Trends Math., Birkhäuser/Springer, Basel (2012), 1–94. 10.1007/978-3-0348-0417-2_1Search in Google Scholar
[15] V. V. Kisil, Geometry of Möbius Transformations, Imperial College Press, London, 2012. 10.1142/p835Search in Google Scholar
[16] V. V. Kisil, Calculus of operators: covariant transform and relative convolutions, Banach J. Math. Anal. 8 (2014), no. 2, 156–184. 10.15352/bjma/1396640061Search in Google Scholar
[17] J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. 10.1002/cpa.3160180121Search in Google Scholar
[18] R. L. Lipsman, Non-Abelian Fourier analysis, Bull. Sci. Math. (2) 98 (1974), no. 4, 209–233. Search in Google Scholar
[19] S. Molahajloo, K. A. Okoudjou and G. E. Pfander, Boundedness of multilinear pseudo-differential operators on modulation spaces, J. Fourier Anal. Appl. 22 (2016), no. 6, 1381–1415. 10.1007/s00041-016-9461-2Search in Google Scholar
[20] S. Molahajloo and M. Pirhayati, Traces of pseudo-differential operators on compact and Hausdorff groups, J. Pseudo-Differ. Oper. Appl. 4 (2013), no. 3, 361–369. 10.1007/s11868-013-0074-0Search in Google Scholar
[21] S. Molahajloo and K. L. Wong, Pseudo-differential operators on finite Abelian groups, J. Pseudo-Differ. Oper. Appl. 6 (2015), no. 1, 1–9. 10.1007/s11868-015-0108-xSearch in Google Scholar
[22] M. W. Wong, Wavelet Transforms and Localization Operators, Oper. Theory Adv. Appl. 136, Birkhäuser, Basel, 2002. 10.1007/978-3-0348-8217-0Search in Google Scholar
[23] M. W. Wong, An Introduction to Pseudo-differential Operators, 3rd ed., Ser. Anal. Appl. Comput. 6, World Scientific, Hackensack, 2014. 10.1142/9074Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
- Infinite families of equivariantly formal toric orbifolds
- Bounds for GL3L-functions in depth aspect
- Nonlinear Dirichlet problems with unilateral growth on the reaction
- K-invariant cusp forms for reductive symmetric spaces of split rank one
- Cellularity in quotient spaces of topological groups
- Shifted convolution sums for higher rank groups
- Dimension quotients, Fox subgroups and limits of functors
- Large sums of Hecke eigenvalues of holomorphic cusp forms
- K-theory classification of graded ultramatricial algebras with involution
- Regularity of symbolic powers and arboricity of matroids
- On some problems concerning symmetrization operators
- An Erdős–Ko–Rado result for sets of pairwise non-opposite lines in finite classical polar spaces
- Rankin–Selberg gamma factors of level zero representations of GLn
- Sobolev’s inequality for double phase functionals with variable exponents
- Independence of Artin L-functions
- Oscillatory singular integral operators with Hölder class kernels on Hardy spaces
Articles in the same Issue
- Frontmatter
- Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
- Infinite families of equivariantly formal toric orbifolds
- Bounds for GL3L-functions in depth aspect
- Nonlinear Dirichlet problems with unilateral growth on the reaction
- K-invariant cusp forms for reductive symmetric spaces of split rank one
- Cellularity in quotient spaces of topological groups
- Shifted convolution sums for higher rank groups
- Dimension quotients, Fox subgroups and limits of functors
- Large sums of Hecke eigenvalues of holomorphic cusp forms
- K-theory classification of graded ultramatricial algebras with involution
- Regularity of symbolic powers and arboricity of matroids
- On some problems concerning symmetrization operators
- An Erdős–Ko–Rado result for sets of pairwise non-opposite lines in finite classical polar spaces
- Rankin–Selberg gamma factors of level zero representations of GLn
- Sobolev’s inequality for double phase functionals with variable exponents
- Independence of Artin L-functions
- Oscillatory singular integral operators with Hölder class kernels on Hardy spaces
