Publications of the Research Institute for Mathematical Sciences

Some applications of Boolean valued set theory to abstract harmonic analysis on locally compact groups

Hirokazu Nishimura

Source: Publ. Res. Inst. Math. Sci. Volume 21, Number 1 (1985), 181-190.

Primary Subjects: 03E40
Secondary Subjects: 22D10, 43A35

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.prims/1195179842
Mathematical Reviews number (MathSciNet): MR780893
Zentralblatt MATH identifier: 0582.43005
Digital Object Identifier: doi:10.2977/prims/1195179842

References

[1] Berberian, S. K., Measure and integration, Chelsea, New York, 1965.
Mathematical Reviews (MathSciNet): MR183839
Zentralblatt MATH: 0233.28001
[2] Berberian, S. K., Notes on spectral theory, Van Nostrand, Princeton, 1966.
Mathematical Reviews (MathSciNet): MR190760
Zentralblatt MATH: 0138.39104
[3] Bochner, S., Vorlesungen uber Fouriesche Integrate, Chelsea, New York, 1948.
Jahrbuch database (Zbl): 58.0292.01
[4] Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Wiley, New York, 1962.
Mathematical Reviews (MathSciNet): MR144979
Zentralblatt MATH: 0131.25601
[5] Eda, K., Reducible lattices and Boolean extensions, preprint.
[6] Godement, R., Les fonctions de type positif et la theorie des groupes, Trans. Amer. Math. Soc., 63 (1948), 1-89.
Mathematical Reviews (MathSciNet): MR23243
Zentralblatt MATH: 0031.35903
[7] Godement, R., Sur la thgorie des representations unitaires, Ann. of Math., 53 (1951), 68-124.
Mathematical Reviews (MathSciNet): MR38571
Zentralblatt MATH: 0042.34606
[8] Godement, R., Memoire sur la theorie des caracteres dans les groupes localement compacts unimodulaires, J. Math. Pures Appl. (9), 30 (1951), 1-110.
Mathematical Reviews (MathSciNet): MR41857
Zentralblatt MATH: 0055.02103
[9] Hewitt, E. and Ross, A., Abstract harmonic analysis I and II, Springer, Berlin, 1963 and 1970.
Zentralblatt MATH: 0115.10603
[10] Jech, T., Set theory, Academic Press, New York, 1978.
Mathematical Reviews (MathSciNet): MR506523
Zentralblatt MATH: 0419.03028
[11] Keiley, 1. L., General topology, Van Nostrand, Princeton, 1955.
Mathematical Reviews (MathSciNet): MR70144
Zentralblatt MATH: 0066.16604
[12] Mackey, G. W., Functions on locally compact groups, Bull. Amer. Math. Soc., 86 (1950), 385-412.
Mathematical Reviews (MathSciNet): MR39729
Zentralblatt MATH: 0045.31301
[13] Mautner, F. I., Unitary representations of locally compact groups I and II, Ann. of Math., 51 (1950), 1-25 and 52 (1950), 528-556.
Mathematical Reviews (MathSciNet): MR32650
Zentralblatt MATH: 0039.02201
[14] Naimark, M. A., Normed algebras, Wolters-Noordhoff, Groningen, 1972.
Mathematical Reviews (MathSciNet): MR438123
Zentralblatt MATH: 0254.46025
[15] Nishimura, H., An approach to the dimension theory of continuous geometry from the standpoint of Boolean valued analysis, to appear in Publ. RIMS.
Mathematical Reviews (MathSciNet): MR764350
Zentralblatt MATH: 0574.51012
[16] Ozawa, M., Boolean valued interpretation of Hilbert space theory, J. Math. Soc. Japan, 35 (1983), 609-627.
Mathematical Reviews (MathSciNet): MR714464
Zentralblatt MATH: 0526.46069
[17] Rickart, C. E., General theory of Banach algebras, Van Nostrand, Princeton, 1960.
Mathematical Reviews (MathSciNet): MR115101
Zentralblatt MATH: 0095.09702
[18] Segal, I. E., The two-sided regular representation of a unimodular locally compact group, Ann. of Math., 51 (1950), 293-298.
Mathematical Reviews (MathSciNet): MR36764
Zentralblatt MATH: 0039.02103
[19] Segal, I. E., An extension of Plancherel's formula to separable unimodular groups, Ann. of Math., 52 (1950), 272-292.
Mathematical Reviews (MathSciNet): MR36765
Zentralblatt MATH: 0045.38502
[20] Takeuti, G. and Zaring, W. M., Axiomatic set theory, Springer, Berlin, 1973.
Mathematical Reviews (MathSciNet): MR416914
Zentralblatt MATH: 0261.02038
[21] Takeuti, G., Two applications of logic to mathematics, Iwanami and Princeton Univ. Press, Tokyo and Princeton, 1978.
Mathematical Reviews (MathSciNet): MR505474
Zentralblatt MATH: 0393.03027
[22] Takeuti, G., A transfer principle in harmonic analysis, J. Symbolic Logic, 44 (1979), 417-440.
Mathematical Reviews (MathSciNet): MR540672
Zentralblatt MATH: 0427.03047
[23] Takeuti, G., Boolean valued analysis, Lecture Notes in Math., 753, pp. 714-731, Springer, Berlin, 1979.
Mathematical Reviews (MathSciNet): MR555569
Zentralblatt MATH: 0427.03046
[24] Takeuti, G., Boolean completion and m-convergence, Lecture Notes in Math., 915, pp. 333- 350, Springer, Berlin, 1982.
Mathematical Reviews (MathSciNet): MR659902
Zentralblatt MATH: 0478.03027
[25] Takeuti, G., Von Neumann algebras and Boolean valued analysis, J. Math. Soc. Japan, 35 (1983), 1-21.
Mathematical Reviews (MathSciNet): MR679070
Zentralblatt MATH: 0488.46052
[26] Tomita, M., Harmonic analysis on locally compact groups, Math. J. Okayama Univ., 5 (1956), 133-193.
Mathematical Reviews (MathSciNet): MR82625
Zentralblatt MATH: 0072.12502
[27] Tsuji, K., Harmonic analysis on locally compact groups, Bull. Kyushu Inst. Tech., 2 (1956), 16-32.
Mathematical Reviews (MathSciNet): MR82626
Zentralblatt MATH: 0075.28504
[28] Yoshizawa, H., Unitary representations of locally compact groups, Osaka Math. J., 1 (1949), 81-89.
Mathematical Reviews (MathSciNet): MR30534
Zentralblatt MATH: 0037.01601
[29] Yoshizawa, H., On some types of convergence of positive definite functions, Osaka Math. J., 1 (1949), 90-94.
Mathematical Reviews (MathSciNet): MR30535
Zentralblatt MATH: 0037.01602
[30] Yoshizawa, H., A proof of the Plancherel theorem, Proc. Japan Acad., 30 (1954), 276-281.
Mathematical Reviews (MathSciNet): MR65824
Zentralblatt MATH: 0057.09802
[31] Zygmund, A., Trigonometric Series, 2nd ed., Cambridge University Press, Cambridge, 1959.
Mathematical Reviews (MathSciNet): MR107776
Zentralblatt MATH: 0367.42001

2009 © Research Institute for Mathematical Sciences

Publications of the Research Institute for Mathematical Sciences

Publications of the Research Institute for Mathematical Sciences