Extension and Interpolation of Linear Operators and Matrix Functions (Operator Theory: Advances and Applications, 47)

Extension and Interpolation of Linear Operators and Matrix Functions (Operator Theory Advances and Applications)

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Extension and Interpolation of Linear Operators and Matrix Functions (Operator Theory: Advances and Applications, 47)

Extension and Interpolation of Linear Operators and Matrix Functions (Operator Theory Advances and Applications)

Written by Israel Gohberg
4.85 25,525 ratings
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About this ebook:
The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e. , a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre­ spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1 , (1. 1) where "the load" SL(Z) is again a Schur function and _ [A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z) ::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = [a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i,j=l, . . .

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Published September 21, 1990
ISBN 14647756
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Israel Gohberg
About the Author
Israel Gohberg

Israel Gohberg writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Israel Gohberg lives with their spouse and a very vocal rescue cat.

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Steven Torres
Steven Torres June 15, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Andrew King January 03, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Karen Smith October 26, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Nancy Lewis February 14, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Christopher Torres December 18, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Sarah Mitchell May 26, 2024
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Donna Smith November 05, 2025
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Michael Johnson February 15, 2025
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John  Parker
John Parker May 04, 2025
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Daniel Evans
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Karen Young
Karen Young July 20, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Emily Martin
Emily Martin March 07, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Donna Flores
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
William Nguyen
William Nguyen January 01, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Sandra Nelson
Sandra Nelson July 19, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Donald Gonzalez
Donald Gonzalez April 22, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Matthew Thomas
Matthew Thomas February 15, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Lisa Jones November 24, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Ashley Rivera
Ashley Rivera April 21, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Emily Smith
Emily Smith May 13, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Lisa Gomez
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Michael White
Michael White May 05, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Christopher King
Christopher King October 07, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Steven Turner
Steven Turner November 02, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
James Martinez
James Martinez June 10, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Matthew Martin
Matthew Martin July 27, 2025
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Emily Robinson
Emily Robinson December 05, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Edward Cruz
Edward Cruz November 29, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Robert Perez
Robert Perez January 10, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Daniel  Parker
Daniel Parker March 20, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Lisa Jones
Lisa Jones July 07, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Michelle Wilson
Michelle Wilson November 01, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
John Rodriguez
John Rodriguez October 18, 2024
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Christopher Gomez
Christopher Gomez November 19, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Lisa Collins
Lisa Collins October 20, 2025
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Betty Hall
Betty Hall December 14, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Elizabeth Nelson
Elizabeth Nelson November 30, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Barbara Reyes
Barbara Reyes July 22, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Jennifer Gonzalez
Jennifer Gonzalez January 08, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
John Garcia
John Garcia July 10, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Elizabeth Martin
Elizabeth Martin April 23, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Patricia Campbell
Patricia Campbell March 04, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Paul Campbell
Paul Campbell November 23, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Deborah Lopez
Deborah Lopez December 07, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Melissa Anderson
Melissa Anderson February 28, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Ashley Edwards
Ashley Edwards February 18, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Ashley Edwards
Ashley Edwards October 21, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Margaret Nguyen
Margaret Nguyen March 31, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Brian Roberts
Brian Roberts January 28, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Barbara Hill
Barbara Hill October 31, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Elizabeth Mitchell
Elizabeth Mitchell June 17, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Nancy Hall
Nancy Hall September 14, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Stephanie Davis January 17, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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