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Acknowledgements I want to express my deepest gratitude to my advisor Matti Vuorinen for his guidance and helpful support throughout my postgraduate years, and in particular for his engagement in helping me preparing this thesis. Matti has shown me what it means to do mathematics in a purposeful and linear working pace, without relinquishing the claim of creativity. I address my sincerest thanks to my teachers throughout the years, in particular my pregraduate advisor S¨oren Illman, who taught me that “mathematics sometimes is ninety per cent work and only ten per cent inspiration”. Special thanks also to Olli Martio and Jussi V¨ais¨al¨a, whom I occasionally have consulted with questions regarding my work, and who at those times have given me useful and inspiring ideas. Thanks also to David Herron, who convinced me that Theorem 5.22 is true. I want to thank also Pekka Alestalo and Raimo N¨akki for their work in the pre-examination of my thesis. Without mentioning anyone particular, I would like to thank my fellow postgraduate students and my colleagues at the department for inspiring discussions – both regarding mathematical and more common subjects – and a great working environment. I am also indebted to the Department of Mathematics and Statistics of the University of Helsinki, and for financial support to the Finnish Academy of Science and Letters (Vilho, Kalle ja Yrj¨o V¨ais¨al¨an s¨a¨ati¨o), the Finnish Cultural Foundation and Nylands Nation vid Helsingfors Universitet. Thanks to all my friends for not arranging too many social events to keep me away from my research (some have done a good job trying though). Finally I’d like to thank my parents and my family for supporting my scientific efforts in every way possible. Helsinki, October 2005 Henri Lind´en
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