Topics in Hardy Classes and Univalent Functions (Birkhuser Advanced Texts Basler Lehrbcher),Used

Topics in Hardy Classes and Univalent Functions (Birkhuser Advanced Texts Basler Lehrbcher),Used

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These notes are based on lectures given at the University of Virginia over the past twenty years. They may be viewed as a course in function theory for nonspecialists. Chapters 16 give the functiontheoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. These chapters were written first, and they were origi nally intended to be a part of that book. Halfplane function theory continues to be useful for applications and is a focal point in our account (Chapters 5 and 6). The theory of Hardy and Nevanlinna classes is derived from proper ties of harmonic majorants of subharmonic functions (Chapters 3 and 4). A selfcontained treatment of harmonic and subharmonic functions is included (Chapters 1 and 2). Chapters 79 present concepts from the theory of univalent functions and Loewner families leading to proofs of the Bieberbach, Robertson, and Milin conjectures. Their purpose is to make the work of de Branges accessible to students of operator theory. These chapters are by the second author. There is a high degree of independence in the chapters, allowing the material to be used in a variety of ways. For example, Chapters 56 can be studied alone by readers familiar with function theory on the unit disk. Chapters 79 have been used as the basis for a onesemester topics course.

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