Analytic Capacity And Measure
by J. Garnett /
1972 / English / PDF
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In some instances a theorem has Il. person's name lI.ttaclled to :it, often simply because that is what the theorem is called. But no doubt some important results have not been ascribed to their Orl ginals, and unattributed theorems shoul d not be Assumed the author's discovery. Throughout each chapter there are exercises and problems. Some exercises are very routine, and sane problems are old and famous, but the only real distinction is that I think I can do the exercises. Chapter I is an exposition of the theory of analytic capacity. It begins at the beginning, and thus has some overla.p with other sources. Chapter II concerns the caUChy integral representation. It contains a simple characterization of Cauchy transforms. The relation between bounded analytic functions, Hausdorff measure, and Newtonian potential theory is taken up in Chapter III. In Chapter IV we discuss three examples, and in Chapter V applica.tions are made to approximation theory. I wish to thank H. Alexander, A. Davie, L. Hedberg, P. Koosis, K. Pietz, H. Royden, J. Wermer and L. Zalcman for valuable suggestions and conversations. I am especial.ly grateful to T. Gamelin for a.dvice at every stage of the preparation of this paper. I also thank Laurie Beerman for typing t1Je manuscript.
