"The special importance of this book, in my opinion, is that it links different investigations from various branches of science: physics, mathematics, chemistry, medicine, and numerical analysis. Moreover, the book also addresses similar problems from engineering. It is clearly shown that a number of phenomena that seemed not to be directly connected, actually are, and this realization is expected to spur progress in many areas. Most importantly, the applicability and superiority of the presented spectral methods are demonstrated. The book is superbly written, and it is self-contained, so that it can be treated as a fundamental source of information for researchers and students in a wide range of fields. Therefore, I strongly recommend this book to colleagues and students."-Professor Ivan Mancev"The present book concerns one of the most beautiful and useful developments in mathematics. It takes the reader from the classical moment problem of Stieltjes via Pade's rational representations, using Hankel determinants and Frobenius normal forms, through the Krylov-Lanczos development to modern algorithmic techniques and codes. The deeper algebraic connections between signal processing and quantum mechanics are implicit and leaven important concrete applications typical of the interdisciplinary faculties of physics and medicine."-Professor Erkki Brandas

• Preface, General Introduction, Direct Link of Spectral Analysis with Eigenvalue Problems in Quantum Physics, Ubiquitous Padé Approximant across Quantum Physics and Signal processing, Versatile Lanczos Methods for Nearest Neighbour Interactions, Synergistic Combination of the Padé and Lanczos Methodologies, First Exact analytical Padé Method and continued Fractions, Algorithmic Strengths of Methods of Moments in Physics and Mathematics, Proof-of-Principle Illustrations of Quantum-mechanical Signal Processing, General Conclusions,Outlook for Quantum-mechanical Processing of generic time signals, Appendices, References

"The special importance of this book, in my opinion, is that it links different investigations from various branches of science: physics, mathematics, chemistry, medicine, and numerical analysis. Moreover, the book also addresses similar problems from engineering. It is clearly shown that a number of phenomena that seemed not to be directly connected, actually are, and this realization is expected to spur progress in many areas. Most importantly, the applicability and superiority of the presented spectral methods are demonstrated. The book is superbly written, and it is self-contained, so that it can be treated as a fundamental source of information for researchers and students in a wide range of fields. Therefore, I strongly recommend this book to colleagues and students."-Professor Ivan Mancev"The present book concerns one of the most beautiful and useful developments in mathematics. It takes the reader from the classical moment problem of Stieltjes via Pade's rational representations, using Hankel determinants and Frobenius normal forms, through the Krylov-Lanczos development to modern algorithmic techniques and codes. The deeper algebraic connections between signal processing and quantum mechanics are implicit and leaven important concrete applications typical of the interdisciplinary faculties of physics and medicine."-Professor Erkki Brandas

• Preface, General Introduction, Direct Link of Spectral Analysis with Eigenvalue Problems in Quantum Physics, Ubiquitous Padé Approximant across Quantum Physics and Signal processing, Versatile Lanczos Methods for Nearest Neighbour Interactions, Synergistic Combination of the Padé and Lanczos Methodologies, First Exact analytical Padé Method and continued Fractions, Algorithmic Strengths of Methods of Moments in Physics and Mathematics, Proof-of-Principle Illustrations of Quantum-mechanical Signal Processing, General Conclusions,Outlook for Quantum-mechanical Processing of generic time signals, Appendices, References

"The special importance of this book, in my opinion, is that it links different investigations from various branches of science: physics, mathematics, chemistry, medicine, and numerical analysis. Moreover, the book also addresses similar problems from engineering. It is clearly shown that a number of phenomena that seemed not to be directly connected, actually are, and this realization is expected to spur progress in many areas. Most importantly, the applicability and superiority of the presented spectral methods are demonstrated. The book is superbly written, and it is self-contained, so that it can be treated as a fundamental source of information for researchers and students in a wide range of fields. Therefore, I strongly recommend this book to colleagues and students."-Professor Ivan Mancev"The present book concerns one of the most beautiful and useful developments in mathematics. It takes the reader from the classical moment problem of Stieltjes via Pade's rational representations, using Hankel determinants and Frobenius normal forms, through the Krylov-Lanczos development to modern algorithmic techniques and codes. The deeper algebraic connections between signal processing and quantum mechanics are implicit and leaven important concrete applications typical of the interdisciplinary faculties of physics and medicine."-Professor Erkki Brandas

• Preface, General Introduction, Direct Link of Spectral Analysis with Eigenvalue Problems in Quantum Physics, Ubiquitous Padé Approximant across Quantum Physics and Signal processing, Versatile Lanczos Methods for Nearest Neighbour Interactions, Synergistic Combination of the Padé and Lanczos Methodologies, First Exact analytical Padé Method and continued Fractions, Algorithmic Strengths of Methods of Moments in Physics and Mathematics, Proof-of-Principle Illustrations of Quantum-mechanical Signal Processing, General Conclusions,Outlook for Quantum-mechanical Processing of generic time signals, Appendices, References