# zbMATH — the first resource for mathematics

On the role of the Heisenberg group in harmonic analysis. (English) Zbl 0442.43002

##### MSC:
 43-02 Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis 43A45 Spectral synthesis on groups, semigroups, etc. 58J40 Pseudodifferential and Fourier integral operators on manifolds 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 22-02 Research exposition (monographs, survey articles) pertaining to topological groups
Full Text:
##### References:
 [1] Richard Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1 – 42. · Zbl 0343.35078 [2] Alberto-P. Calderón and Rémi Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan 23 (1971), 374 – 378. · Zbl 0203.45903 [3] Pierre Cartier, Quantum mechanical commutation relations and theta functions, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 361 – 383. [4] Ronald G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 49. · Zbl 0247.47001 [5] A. Grossmann, G. Loupias, and E. M. Stein, An algebra of pseudodifferential operators and quantum mechanics in phase space, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 343 – 368, viii (1969) (English, with French summary). · Zbl 0176.45102 [6] L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), no. 3, 360 – 444. · Zbl 0388.47032 [7] Roger Howe, On some results of Strichartz and Rallis and Schiffman, J. Funct. Anal. 32 (1979), no. 3, 297 – 303. · Zbl 0408.22018 [8] R. Howe, Remarks on Huyghens’ principle (preprint). [9] Roger Howe, Quantum mechanics and partial differential equations, J. Funct. Anal. 38 (1980), no. 2, 188 – 254. · Zbl 0449.35002 [10] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57 – 110 (Russian). · Zbl 0090.09802 [11] A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489 – 578. · Zbl 0257.22015 [12] J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269 – 305. · Zbl 0171.35101 [13] Serge Lang, \?\?$$_{2}$$(\?), Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. · Zbl 0583.22001 [14] S. Lang, Real analysis, Addison-Wesley, Reading, Mass., 1969. [15] George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265 – 311. · Zbl 0082.11301 [16] Calvin C. Moore and Joseph A. Wolf, Square integrable representations of nilpotent groups, Trans. Amer. Math. Soc. 185 (1973), 445 – 462 (1974). · Zbl 0274.22016 [17] D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287 – 354. · Zbl 0219.14024 [18] Stephen Rallis and Gérard Schiffmann, Weil representation. I. Intertwining distributions and discrete spectrum, Mem. Amer. Math. Soc. 25 (1980), no. 231, iii+203. · Zbl 0442.22006 [19] I. E. Segal, Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand. 13 (1963), 31 – 43. · Zbl 0208.39002 [20] David Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103 (1962), 149 – 167. · Zbl 0171.46901 [21] Robert S. Strichartz, Fourier transforms and non-compact rotation groups, Indiana Univ. Math. J. 24 (1974/75), 499 – 526. · Zbl 0295.42015 [22] François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. · Zbl 0171.10402 [23] U. Venugopalkrishna, Fredholm operators associated with strongly pseudoconvex domains in \?$$^{n}$$, J. Functional Analysis 9 (1972), 349 – 373. · Zbl 0241.47023 [24] J. v. Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren, Math. Ann. 104 (1931), no. 1, 570 – 578 (German). · JFM 57.1446.01 [25] André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143 – 211 (French). · Zbl 0203.03305 [26] H. Weyl, The theory of groups and quantum mechanics, Methuen, London, 1931. · JFM 58.1374.01 [27] Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. · Zbl 1024.20501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.