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Axiomatic Set Theory. 2nd ed. 34 SPITZER. Principles of Random Walk. 2 OXTOBY. Measure and Category. 2nd ed. 2nded. 3 SCHAEFER. Topological Vector Spaces. 35 ALEXANDERiWERMER. Several Complex 2nded. Variables and Banach Algebras. 3rd ed. 4 HILTON/STAMMBACH. A Course in 36 KELLEy/NAMIOKA et al. Linear Topological Homological Algebra. 2nd ed. Spaces. 5 MAc LANE. Categories for the Working 37 MONK. Mathematical Logic. Mathematician. 2nd ed. 38 GRAUERTIFRITZSCHE. Several Complex 6 HUGHES/PIPER. Projective Planes. Variables. 7 SERRE. A Course in Arithmetic. 39 ARVESON. An Invitation to C*-Algebras. 8 TAKEUTriZARING. Axiomatic Set Theory. 40 KEMENY/SNELLiKNAPP. Denumerable 9 HUMPHREYS. Introduction to Lie Algebras Markov Chains. 2nd ed. and Representation Theory. 41 ApOSTOL. Modular Functions and Dirichlet 10 COHEN. A Course in Simple Homotopy Series in Number Theory. Theory. 2nd ed. II CONWAY. Functions of One Complex 42 SERRE. Linear Representations of Finite Variable I. 2nd ed. Groups. 12 BEALS. Advanced Mathematical Analysis. 43 GILLMAN/JERISON. Rings of Continuous 13 ANDERSON/FULLER. Rings and Categories Functions. of Modules. 2nd ed. 44 KENDIG. Elementary Algebraic Geometry. 14 GOLUBITSKy/GUlLLEMIN. Stable Mappings 45 LOEVE. Probability Theory I. 4th ed. and Their Singularities. 46 LOEVE. Probability Theory II. 4th ed. 15 BERBERIAN. Lectures in Functional 47 MOISE. Geometric Topology in Analysis and Operator Theory. Dimensions 2 and 3. 16 WINTER. The Structure of Fields. 48 SACHS/WU. General Relativity for 17 ROSENBLATT. Random Processes. 2nd ed. Mathematicians. 18 HALMOS. Measure Theory. 49 GRUENBERG/WEIR. Linear Geometry. 19 HALMOS. A Hilbert Space Problem Book. 2nd ed. 2nded. 50 EDWARDS. Fermat's Last Theorem. 20 HUSEMOLLER. Fibre Bundles. 3rd ed. 51 KLINGENBERG. A Course in Differential 21 HUMPHREYS. Linear Algebraic Groups. Geometry. 22 BARNES/MACK. An Algebraic Introduction 52 HARTSHORNE. Algebraic Geometry. to Mathematical Logic. 53 MANIN. A Course in Mathematical Logic. 23 GREUB. Linear Algebra. 4th ed. 54 GRAVERiW ATKINS. Combinatorics with 24 HOLMES. Geometric Functional Analysis Emphasis on the Theory of Graphs. and Its Applications.

In this chapter, we collect several preliminary results about entire functions, lattices in the complex plane, pseudodifferential operators, and the Heisenberg group. The purpose is to fix notation and to facilitate references later on. All the results concerning entire functions, except Lindelöf's theorem, are well known and elementary. The section about Weierstrass σ -functions is self-contained, while the section on pseudodifferential operators is very sketchy.

ABSTRACT. There has been a great deal of work done in recent years on weighted Bergman spaces A p α on the unit ball B n of C n , where 0 < p < ∞ and α > −1. We extend this study in a very natural way to the case where α is any real number and 0 < p ≤ ∞. This unified treatment covers all classical Bergman spaces, Besov spaces, Lipschitz spaces, the Bloch space, the Hardy space H 2 , and the so-called Arveson space. Some of our results about integral representations, complex interpolation, coefficient multipliers, and Carleson measures are new even for the ordinary (unweighted) Bergman spaces of the unit disk.

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Abstract. We give a new and simple compactness criterion for composition operators C ϕ on BMOA and the Bloch space in terms of the norms of ϕ n in the respective spaces.

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