Rational Approximation Schemes for Solutions of Abstract Cauchy Problems and Evolution Equations

Acknowledgments It is a great pleasure to thank Professor Frank Neubrander for the suggestion of the topic, his continuous support and unique style of guidance over the years. It is also a pleasure to thank the Department of Mathematics and the Graduate School of Louisiana State University for the generous financial support. I would also like to thank to Prof. for their hospitality, valuable support, and interesting discussions. I extend the most sincere gratitude to Zito for their friendship and support since I arrived to LSU. Also, I would like to thank my friends and colleagues Bacim Alali, Alvaro Guevara, Jasson Vindas, and Kevin Zito for their moral support and the exciting discussions concerning mathematics and life in general. Finally, I would like to express my deepest gratitude to my family whose support and understanding has been invaluable over all these years. This dissertation is dedicated to the memory of my father Galvarino Jara (1942–1981) and my grandfather Pablo Tapia (1916–2007). It was their vision, effort, and encouragement which allowed me to achieve my dreams.

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