Directional time-frequency analysis with applications

The undersigned, appointed by the Dean of the Graduate School, have examined the dissertation entitled DIRECTIONAL TIME-FREQUENCY ANALYSIS WITH APPLICATIONS presented by Christopher Sansing, a candidate for the degree of Doctor of Philosophy, and hereby certify that in their opinion it is worthy of acceptance. To Allie Rose. ACKNOWLEDGMENTS It is impossible to thank, in only a few pages, all the people who have helped this dis-sertation come to fruition. I will attempt to thank as many as possible and apologize for anyone inadvertently left out. I would first like to thank my graduate advisor, Loukas Grafakos. Without his support and many mathematical conversations, this research would not be possible. He first introduced me to the pure and applied world of harmonic analysis and I have been hooked ever since. His passion for mathematics and research has pushed me forward and has given me a great example of constantly striving for academic excellence. My advisor also taught a lot of the graduate classes which I attended while in graduate school, including basic preparation courses for the qualifying exams and more advanced courses like harmonic analysis. I can say from a lot of experience that he is an excellent teacher and I owe a lot of my mathematical knowledge to him. Finally, I would like to thank him for all of his advice and the hospitality he has shown to me during my time at the University of Missouri. Evan Boote; who have been very supportive and helpful during my time preparing this work. I would like to especially thank Pete Casazza for many discussions which I have benefited from. He was an excellent source for many questions on frame theory and different mathematical applications. We also had many fruitful discussions about the teaching of mathematics in general. Another person to which I owe thanks is Yuri Latushkin who was the Director of Graduate Studies when I started graduate school and has been a source of excellent advice. He also introduced me to the annual TULKA internet seminar which I took part of and learned a lot from. Special thanks are also due to Loukas Grafakos and Nigel Kalton for financial support during my summers here. I would also like to collectively thank the mathematics department at the University of Missouri for the hospitality shown to me and the chance to pursue my graduate education here. There are many special people …