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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Preface.........................................................................................................5
1. Introduction...............................................................................................6
1.1. Measurability and vector measures.....................................................6
1.2. Convolution and vector measures.....................................................12
1.3. Operator-valued measures................................................................14
2. Harmonic analysis....................................................................................17
2.1. Commutative harmonic analysis for vector-valued functions...............17
3. Convolution with respect to operator-valued measures...........................24
3.1. General theory....................................................................................24
3.2. Vector-valued p-multipliers..................................................................28
3.3. Characterising operator-valued Fourier-Stieltjes transforms..............44
3.4. Strong 1-multipliers.............................................................................47
3.5. Locally compact groups in general: Wendel's theorem.......................54
3.6. Costé's theorem..................................................................................57
4. Convolution with respect to spectral measures........................................60
4.1. General theory....................................................................................60
4.2. Translation: the canonical spectral measure on L²(G)........................65
4.3. Applications........................................................................................72
References..................................................................................................74
Index............................................................................................................76
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
385
Liczba stron
77
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXXV
Daty
wydano
2000
otrzymano
1999-03-08
poprawiono
1999-10-19
Twórcy
autor
- School of Mathematics, University of NSW, Sydney, NSW 2052, Australia
autor
- School of Mathematics, University of NSW, Sydney, NSW 2052, Australia
autor
- School of Mathematics, University of NSW, Sydney, NSW 2052, Australia
Bibliografia
- [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
- [2] S. Bochner, A theorem on Fourier-Stieltjes integrals, Bull. Amer. Math. Soc. 40 (1934), 271-276.
- [3] P. Brenner, The Cauchy problem for symmetric hyperbolic systems in $L_p$, Math. Scand. 19 (1966), 27-37.
- [4] Z. Bukovská, Characterization of Fourier transforms of vector valued functions and measures, Mat. Časopis 20 (1970), 109-115.
- [5] J. Diestel and J. J. Uhl Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, RI, 1977.
- [6] N. Dinculeanu, Vector Measures, Pergamon Press, London, 1967.
- [7] I. Dobrakov, On integration in Banach spaces I, Czechoslovak Math. J. 20 (1970), 511-536.
- [8] W. F. Eberlein, Characterization of Fourier-Stieltjes transforms, Duke Math. J. 22 (1955), 465-468.
- [9] R. E. Edwards, Functional Analysis: Theory and Applications, Holt, Rinehart and Winston, New York, 1965.
- [10] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, Berlin, 1977.
- [11] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.
- [12] E. Hewitt, A new proof of Plancherel's theorem for locally compact abelian groups, Acta Sci. Math. (Szeged) 24 (1963), 219-227.
- [13] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis II, Springer, Berlin, 1970.
- [14] E. Hewitt and K. R. Stromberg, A remark on Fourier-Stieltjes transforms, An. Acad. Brasil. Ciênc. 34 (1962), 175-180.
- [15] E. Hewitt and K. R. Stromberg, Real and Abstract Analysis, Springer, Berlin, 1965.
- [16] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Colloq. Publ. 31, Amer. Math. Soc., Providence, RI, 1957.
- [17] B. R. F. Jefferies, An operator bound related to Feynman-Kac formulæ, Proc. Amer. Math. Soc. 122 (1994), 1191-1202.
- [18] S. Kwapień, Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44 (1972), 583-595.
- [19] I. Kluvánek, Characterization of Fourier-Stieltjes transforms of vector and operator valued measures, Czechoslovak Math. J. 17 (92) (1967), 261-276.
- [20] I. Kluvánek, Fourier transforms of vector-valued functions and measures, Studia Math. 37 (1970), 1-12.
- [21] I. Kluvánek and G. Knowles, Vector Measures and Control Systems, North-Holland, Amsterdam, 1976.
- [22] W. Littman, C. McCarthy and N. Rivière, $L^p$-multiplier theorems, Studia Math. 30 (1968), 193-217.
- [23] S. Okada and W. J. Ricker, Uniform operator σ-additivity of indefinite integrals induced by scalar-type spectral operators, Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), 141-146.
- [24] W. Rudin, Fourier Analysis on Groups, 2nd printing, Wiley, New York, 1967.
- [25] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
- [26] H. H. Schaefer, Topological Vector Spaces, 4th ed., Springer, Berlin, 1980.
- [27] J. T. Schwartz, A remark on inequalities of Calderón-Zygmund type for vector-valued functions, Comm. Pure Appl. Math. 14 (1961), 785-799.
- [28] I. E. Segal and R. A. Kunze, Integrals and Operators, McGraw-Hill, New York, 1968.
- [29] A. B. Simon, Cesàro summability on groups: Characterization and inversion of Fourier transforms, in: Function Algebras (Tulane Univ., 1965), 208-215.
- [30] E. M. Stein, Harmonic Analysis, Princeton Univ. Press, 1993.
- [31] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.
- [32] U. B. Tewari, M. Dutta and D. P. Waidya, Multipliers of group algebras of vector-valued functions, Proc. Amer. Math. Soc. 81 (1981), 223-229.
- [33] G. E. F. Thomas, Integration of functions with values in locally convex Suslin spaces, Trans. Amer. Math. Soc. 212 (1975), 61-81.
- [34] G. E. F. Thomas, Totally summable functions with values in locally convex spaces, in: Measure Theory (Oberwolfach, 1975), Lecture Notes in Math. 541, Springer, Berlin, 1976, 117-131.
- [35] J. L. Torrea, Multipliers for vector valued functions, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 137-143.
- [36] J. G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific J. Math. 2 (1952), 251-261.
- [37] J. Wermer, Commuting spectral operators in Hilbert space, Pacific J. Math. 4 (1954), 355-361.
- [38] J. S. W. Wong, On a characterization of Fourier transforms, Monatsh. Math. 70 (1966), 74-80.
- [39] A. C. Zaanen, Integration, North-Holland, Amsterdam, 1967.
Języki publikacji
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Uwagi
2000 Mathematics Subject Classification: Primary 46G10, 42B15; Secondary 43A15, 43A05.
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ISSN
0012-3862
Kolekcja
DML-PL
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