Journal of the American Mathematical Society

The analogue of the strong Szegö limit theorem on the 2- and 3-dimensional spheres

Author(s): Kate Okikiolu
Journal: J. Amer. Math. Soc. 9 (1996), 345-372.
MSC (1991): Primary 58G15; Secondary 33C55, 47B35
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1.: R. Doktorski\u{i}, Generalization of the Szegö limit theorem to the multidimensional case, Sibirsk. Mat. Zh. 25 (5) (1984), 20--29; English transl., Siberian Math. J. 25 (1984), 701--710. MR 86g:47027
2.: B. Golinski\u{i} and I. Ibragimov, On Szegö's limit theorem, Math. USSR--Izv. 5 (1971), no. 2, 421--444. MR 45:804
3.: U. Grenader and G. Szegö, Toeplitz forms and their applications, Calif. Mono. in Math. Sci., Univ. of Calif. Press, Berkeley and Los Angeles, 1958. MR 20:1349
4.: I. Hirschman Jr., The strong Szegö limit theorem for Toeplitz determinants, Amer. J. Math. 88 (1966), 577--614. MR 35:2064
5.: L. Hörmander, The analysis of linear partial differential operators, III, Grundlehr. der mathemat. Wissenschaften 275 (1985), Springer Verlag. MR 87d:35002a
6.: K. Johansson, On Szegö's asymptotic formula for Toeplitz determinants and generalizations, Phd Diss., UUDM Report 15, Uppsala Univ. Dept. of Math., Uppsala, Sweden, 1987.
7.: M. Kac, Toeplitz matrices, translation kernels and a related problem in probability theory, Duke Math. J. 21 (1954), 501--509. MR 16:31
8.: A. Laptev and Y. Safarov, Error estimate in the generalized Szegö theorem, Journées: ``Equ. aux Dérivées Partielles'' (Saint Jean de Monts, 1991), Exposé XV, École Polytech., Palaiseau, 1991. MR 92j:35141
9.: I. Linnik, A multidimensional analog of a limit theorem of G. Szegö, Math. USSR Izv. 9 (1975), 1323--1332. MR 54:10958
10.: K. Okikiolu, The analogue of the strong Szegö limit theorem on the torus and the 3-sphere, Ph.d. Diss., Dept. Math UCLA, Los Angeles, California, (1991).
11.: K. Okikiolu, The analogue of the strong Szegö limit theorem for a Sturm-Liouville operator on the interval, preprint, (1992).
12.: E. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, New Jersey, (1971). MR 46:4102
13.: G. Szegö, Orthogonal polynomials, Amer. Math. Soc., Providence, Rhode Island, (1975). MR 51:8724
14.: A. Uribe, A symbol calculus for a class of pseudodifferential operators on $S^{n}$ and band asymptotics, J. Func. Anal. 59 (1984), 535--556. MR 86c:58140
15.: N. Vilenkin, Special functions and the theory of group representations, Transl. of Math. Mono. 22, Amer. Math. Soc., Providence, Rhode Island, (1968). MR 37:5429
16.: H. Widom, Asymptotic expansions for pseudodifferential operators in bounded domains, Lect. Notes in Math. 1152, Springer Verlag, (1985). MR 87d:35156
17.: H. Widom, Szegö's theorem and a complete symbolic calculus for pseudo-differential operators, Seminar on Singularities of Solutions, Princeton Univ. Press, (1979), pp. 261--283. MR 81b:58043

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 58G15, 33C55, 47B35

Kate Okikiolu
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

DOI: 10.1090/S0894-0347-96-00188-9
PII: S 0894-0347(96)00188-9
Received by editor(s): May 24, 1994
Additional Notes: Supported by National Science Foundation grant DMS 9304580.
Copyright of article: Copyright 1996, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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