Regarding an entire function being affineOn maximal ideal spaces of a banach algebraAlgebra of bounded functions on a completely regular spaceIdentity theorem - entire functionEvery Jordan function $phi$ on $A$ is multiplicative.A complex unital algebra which is a Banach space is also a Banach algebraMistake in Bak/Newman — need help figuring this outEntire function and constantWhat space corresponds to the localisation of the ring of continuous functions?On a pseudo periodic entire function being an exponential functionQuestion on entire function
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Regarding an entire function being affine
On maximal ideal spaces of a banach algebraAlgebra of bounded functions on a completely regular spaceIdentity theorem - entire functionEvery Jordan function $phi$ on $A$ is multiplicative.A complex unital algebra which is a Banach space is also a Banach algebraMistake in Bak/Newman — need help figuring this outEntire function and constantWhat space corresponds to the localisation of the ring of continuous functions?On a pseudo periodic entire function being an exponential functionQuestion on entire function
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I have been reading this article A characterization of multiplicative linear functionals in Banach algebras and got stuck in the middle of the proof of theorem 1.2 on page 217.
In the 3rd line from below, they say that the function $f_a,b:mathbbClongrightarrowmathbbC$ is Lipschitz and entire hence it is affine. Can anyone tell me why it would be affine. Or suggest me a reference to the result which states that an Lipschitz entire complex function will be affine.
Or can you tell other conditions for an entire function to be affine?
complex-analysis banach-algebras entire-functions
asked Mar 30 at 5:34
user534666user534666
374
$endgroup$
add a comment |
$begingroup$
I have been reading this article A characterization of multiplicative linear functionals in Banach algebras and got stuck in the middle of the proof of theorem 1.2 on page 217.
In the 3rd line from below, they say that the function $f_a,b:mathbbClongrightarrowmathbbC$ is Lipschitz and entire hence it is affine. Can anyone tell me why it would be affine. Or suggest me a reference to the result which states that an Lipschitz entire complex function will be affine.
Or can you tell other conditions for an entire function to be affine?
complex-analysis banach-algebras entire-functions
asked Mar 30 at 5:34
user534666user534666
374
$endgroup$
$begingroup$
answers.yahoo.com/question/index?qid=20101221090813AA6d8dG
$endgroup$
– Clement C.
Mar 30 at 5:55
add a comment |
$begingroup$
I have been reading this article A characterization of multiplicative linear functionals in Banach algebras and got stuck in the middle of the proof of theorem 1.2 on page 217.
In the 3rd line from below, they say that the function $f_a,b:mathbbClongrightarrowmathbbC$ is Lipschitz and entire hence it is affine. Can anyone tell me why it would be affine. Or suggest me a reference to the result which states that an Lipschitz entire complex function will be affine.
Or can you tell other conditions for an entire function to be affine?
complex-analysis banach-algebras entire-functions
asked Mar 30 at 5:34
user534666user534666
374
$endgroup$
I have been reading this article A characterization of multiplicative linear functionals in Banach algebras and got stuck in the middle of the proof of theorem 1.2 on page 217.
In the 3rd line from below, they say that the function $f_a,b:mathbbClongrightarrowmathbbC$ is Lipschitz and entire hence it is affine. Can anyone tell me why it would be affine. Or suggest me a reference to the result which states that an Lipschitz entire complex function will be affine.
Or can you tell other conditions for an entire function to be affine?
complex-analysis banach-algebras entire-functions
complex-analysis banach-algebras entire-functions
asked Mar 30 at 5:34
user534666user534666
374
asked Mar 30 at 5:34
user534666user534666
374
asked Mar 30 at 5:34
user534666user534666
374
asked Mar 30 at 5:34
user534666user534666
374
asked Mar 30 at 5:34
user534666user534666
374
374
$begingroup$
answers.yahoo.com/question/index?qid=20101221090813AA6d8dG
$endgroup$
– Clement C.
Mar 30 at 5:55
add a comment |
$begingroup$
answers.yahoo.com/question/index?qid=20101221090813AA6d8dG
$endgroup$
– Clement C.
Mar 30 at 5:55
$begingroup$
answers.yahoo.com/question/index?qid=20101221090813AA6d8dG
$endgroup$
– Clement C.
Mar 30 at 5:55
$begingroup$
answers.yahoo.com/question/index?qid=20101221090813AA6d8dG
$endgroup$
– Clement C.
Mar 30 at 5:55
add a comment |
1 Answer
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Since $f_a,b$ is Lipschitz, its derivative is bounded. A bounded entire constant is constant, so $f_a,b$ is an antiderivative of a constant, so it is affine.
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
$endgroup$
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Since $f_a,b$ is Lipschitz, its derivative is bounded. A bounded entire constant is constant, so $f_a,b$ is an antiderivative of a constant, so it is affine.
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
$endgroup$
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
add a comment |
$begingroup$
Since $f_a,b$ is Lipschitz, its derivative is bounded. A bounded entire constant is constant, so $f_a,b$ is an antiderivative of a constant, so it is affine.
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
$endgroup$
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
add a comment |
$begingroup$
Since $f_a,b$ is Lipschitz, its derivative is bounded. A bounded entire constant is constant, so $f_a,b$ is an antiderivative of a constant, so it is affine.
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
$endgroup$
Since $f_a,b$ is Lipschitz, its derivative is bounded. A bounded entire constant is constant, so $f_a,b$ is an antiderivative of a constant, so it is affine.
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
answered Mar 30 at 5:58
Eric WofseyEric Wofsey
192k14220352
192k14220352
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
add a comment |
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
$begingroup$
"Lipschitz and entire" is in the question @ClementC.
$endgroup$
– TomGrubb
Mar 30 at 6:02
add a comment |
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answers.yahoo.com/question/index?qid=20101221090813AA6d8dG
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– Clement C.
Mar 30 at 5:55