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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
1. Introduction...................................................................................................... 5
2. Notation and basic terminology........................................................................... 7
3. Definition and basic properties of the $L_{p,q}$ spaces................................. 11
4. Integral representation of bounded linear functionals on $L_{p,q}(B)$........ 23
5. Examples in $L_{p,q}$ theory................................................................................ 31
6. Structure of the $L_{p,q}$ spaces......................................................................... 37
7. An application in group representation theory.................................................. 57
References.................................................................................................................. 67
1. Introduction...................................................................................................... 5
2. Notation and basic terminology........................................................................... 7
3. Definition and basic properties of the $L_{p,q}$ spaces................................. 11
4. Integral representation of bounded linear functionals on $L_{p,q}(B)$........ 23
5. Examples in $L_{p,q}$ theory................................................................................ 31
6. Structure of the $L_{p,q}$ spaces......................................................................... 37
7. An application in group representation theory.................................................. 57
References.................................................................................................................. 67
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
164
Liczba stron
68
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXIV
Daty
wydano
1980
Twórcy
autor
Bibliografia
- [1] S. K. Berberian, Measure and integration, Macmillan, New York 1965.
- [2] N. Bourbaki, Intégration, Chapitre 7 and 8, Hermann, Paris 1963.
- [3] F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), pp. 97-205.
- [4] M. M. Day, Some more uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), pp. 504-507.
- [5] N. Dinculeanu, Vector measures, Pergamon Press, New York 1967.
- [6] E. Dubinsky, A. Pełczyński and H. P. Rosenthal, On Banach spaces X for which $Π_2(ℒ_∞, X) = B(ℒ_∞, X)$, Studia Math. 44 (1972), pp. 617-648.
- [7] N. Dunford and J. Schwartz, Linear operators, Parts I and II, Interscience, New York 1958 and 1963.
- [8] R. E. Edwards, Functional analysis, Holt, Rinehart and Winston, New York 1965.
- [9] P. R. Halmos, On the set of values of a finite measure, Bull. Amer. Math. Soc. 53 (1947), pp. 138-141.
- [10] P. R. Halmos, Measure theory, van Nostrand, New York 1950.
- [11] E. Hewitt and K. Ross, Abstract harmonic analysis, Vol. I, Springer-Verlag, Berlin 1963.
- [12] A. and C. Ionescu Tulcea, On the existence of a lifting commuting with the left translations of an arbitrary locally compact group, In Proceddings of the Fifth Berkeley Symposium, Vol. II, Part 1, University of California Press, Berkeley 1967, pp. 63-97.
- [13] A. and C. Ionescu Tulcea, Topics in the theory of lifting, Springer-Verlag, New York 1969.
- [14] J. L. Kelley, General topology, van Nostrand, New York 1955.
- [15] A. Kleppner, Intertwining forms for summable induced representations, Trans. Amer. Math. Soc. 12 (1964), pp. 164-183.
- [16] H. Krajlewić, Induced representations of locally compact groups on Banach spaces, Glasnik Mathematićki 4 (1969), pp. 183-195.
- [17] J. Kupka, A new class of Banach spaces associated with a disintegrate measure, Dissertation, University of California, Berkeley 1970.
- [18] J. Kupka, Radon-Nikodym theorems for vector valued measures, Trans. Amer. Math. Soc. 169 (1972), pp. 197-217.
- [19] M. Loève, Probability theory, 3-rd ed., van Nostrand, New York 1963.
- [20] G. Mackey, Induced representations of locally compact groups (I), Ann. Math. 55 (1952), pp. 101-139.
- [21] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. 28 (1942), pp. 108-111.
- [22] J. Neveu, Mathematical foundations of the calculus of probability, Holden-Day, San Francisco 1965.
- [23] B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), pp. 277-304.
- [24] M. A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Funct. Anal. 1 (1967), pp. 443-491.
- [25] H. L. Royden, Beat analysis, 2-nd ed., Macmillan, New York 1968.
- [26] L. Schwartz, Désintégration régulière d'une mesure par rapport à une famille de tribus, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), pp. A424-A425.
- [27] I. E. Segal, Equivalences of measure spaces, Amer. J. Math. 73 (1951),pp. 275-313.
- [28] I. E. Segal, and R. A. Kunze, Integrals and operators, McGraw-Hill, New York 1968.
- [29] J. J. Westman, Harmonic analysis on groupoids, Pacific J. Math. 27 (1968), pp. 621-632.
- [30] H. Widom, Lectures on integral equations, van Nostrand, New York 1969.
- [31] A. C. Zaanen, Linear analysis, Bibliotheca Mathematica, vol. II, P. Noordhoff, N. V., Groningen 1960.
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Identyfikator YADDA
bwmeta1.element.zamlynska-1bd55e8a-85d9-444a-8133-1bf149fa8a08
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ISSN
0012-3862
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83-01-01100-9
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DML-PL
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