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Several Complex Variables II: Function Theory in Classical Domains Complex Potential Theory

Penned By G.M. Khenkin
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Several Complex Variables II: Function Theory in Classical Domains Complex Potential Theory

Penned By G.M. Khenkin
4.85 77,370 Ratings
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Editor's Note:
Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given."

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Released October 14, 1985
Identifier (ISBN) 22648780
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G.M. Khenkin
The Mind Behind the Work
G.M. Khenkin

G.M. Khenkin is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, G.M. Khenkin enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Ashley  Parker
Ashley Parker March 31, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Ashley Clark
Ashley Clark August 07, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
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Thomas Hill
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"Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
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Brian Lewis December 26, 2024
"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Gary Hill
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"A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend."
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Ashley Diaz February 26, 2024
"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Mark Hill
Mark Hill March 13, 2025
"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. 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. I am now a lifelong fan of this author."
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Joshua Hill March 24, 2025
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
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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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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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Amanda Mitchell May 07, 2024
"Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"Honestly one of the most premium reading experiences lately. 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. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
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Michael Gomez November 12, 2025
"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
Joseph Collins
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"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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"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall."
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