Operator analysis : hilbert space methods in complex analysis
Agler, Jim
Operator analysis : hilbert space methods in complex analysis by Jim Agler, John E. McCarthy and Nicholas Young - New York : Cambridge University Press, ©2020 - xv, 375p.; 25 cm. - Cambridge tracts in mathematics 219 .
Includes bibliographical references and index.
1. The origins of operator-theoretic approaches to function theory 2. Operator analysis on D : model formulas, lurking isometries, and positivity arguments 3. Further development of models on the disc 4. Operator analysis on D² 5. Carathéodory-Julia theory on the disc and the bidisc
"The philosophy of this book is that Hilbert space geometry binds function theory and operator theory together, not only allowing each to aid the other, but creating a rich structure that can be used to discover new phenomena. There is a "three-way street" between operator theory and function theory: sometimes one uses function theory to prove operator theorems, sometimes one uses operator theory to prove function theorems, and sometimes the theories are so interwoven that one cannot even state the theorem without using the language of both operator theory and function theory"--
9781108485449
Operator theory.
Holomorphic functions.
Geometric function theory.
Hilbert space.
QA329 / .A384 2019
515.724 / AGL-O
Operator analysis : hilbert space methods in complex analysis by Jim Agler, John E. McCarthy and Nicholas Young - New York : Cambridge University Press, ©2020 - xv, 375p.; 25 cm. - Cambridge tracts in mathematics 219 .
Includes bibliographical references and index.
1. The origins of operator-theoretic approaches to function theory 2. Operator analysis on D : model formulas, lurking isometries, and positivity arguments 3. Further development of models on the disc 4. Operator analysis on D² 5. Carathéodory-Julia theory on the disc and the bidisc
"The philosophy of this book is that Hilbert space geometry binds function theory and operator theory together, not only allowing each to aid the other, but creating a rich structure that can be used to discover new phenomena. There is a "three-way street" between operator theory and function theory: sometimes one uses function theory to prove operator theorems, sometimes one uses operator theory to prove function theorems, and sometimes the theories are so interwoven that one cannot even state the theorem without using the language of both operator theory and function theory"--
9781108485449
Operator theory.
Holomorphic functions.
Geometric function theory.
Hilbert space.
QA329 / .A384 2019
515.724 / AGL-O