Question

An entire and one-to-one function must be of the form AZ+B, A non-zero. How to rule out higher degree polynomials in z?

score 1.4k · Answer 1 · 2014-12-17 22:17:45

1.4k

Views

An entire and one-to-one function must be of the form AZ+B, A non-zero. How to rule out higher degree polynomials in z?

Published on 17 Dec 2014 - 22:17

score 3.2k · Answer 2 · 2014-12-29 17:08:21

3.2k

Views

Proof of the Riesz-Schauder Theorem (for compact operators) using the Analytical Fredholm Theorem

Published on 29 Dec 2014 - 17:08

score 37 · Answer 3 · 2015-01-01 23:04:36

37

Views

Sequence of partial sums converges locally uniformly?

Published on 01 Jan 2015 - 23:04

score 116 · Answer 4 · 2019-10-04 12:13:34

116

Views

Dimension of the solution space of a real analytic system of equations

Published on 04 Oct 2019 - 12:13

score 24 · Answer 5 · 2019-10-07 16:42:18

24

Views

PDE System and Analytic Functions

Published on 07 Oct 2019 - 16:42

score 32 · Answer 6 · 2019-10-07 17:34:21

32

Views

PDE Analytic System

Published on 07 Oct 2019 - 17:34

score 42 · Answer 7 · 2019-10-15 09:54:52

42

Views

A paradox on real vs complex analyticity

Published on 15 Oct 2019 - 9:54

score 138 · Answer 8 · 2019-11-21 13:10:05

138

Views

$f,g$ analytic on $I\subset \mathbb{R}$. If exist $a\in I$ such that $f=g$ and $f^{(n)}=g^{(n)}$then we have $f(x)=g(x)$ for every $x \in I$.

Published on 21 Nov 2019 - 13:10

score 42 · Answer 9 · 2019-11-27 15:52:28

42

Views

Real analyticity of harmonic functions

Published on 27 Nov 2019 - 15:52

score 166 · Answer 10 · 2019-11-28 18:58:08

166

Views

Analytical functions equal at a point implies all derivatives are also equal at that point?

Published on 28 Nov 2019 - 18:58

score 61 · Answer 11 · 2019-11-29 14:26:33

61

Views

Writing $f(x)=h(x)\cdot(x-\alpha)^m$ when $\alpha$ is a root of multiplicity $m$

Published on 29 Nov 2019 - 14:26

score 363 · Answer 12 · 2019-12-06 13:37:11

363

Views

Analytic maps from upper half plane to itself

Published on 06 Dec 2019 - 13:37

score 68 · Answer 13 · 2019-12-11 14:25:01

68

Views

Does here exists an analytic function $f:\mathbb C → \mathbb C$ such that $f(0) = 1, f(4i) = i$...

Published on 11 Dec 2019 - 14:25

score 45 · Answer 14 · 2019-12-13 10:12:15

45

Views

$J(z)= \frac{1}{\pi} \int _0 ^\infty \frac{z}{\eta^2+z^2} \ln (\frac{1}{1-e^{-2\pi \eta}}) d \eta$ is analytic in Re $(z)>0$

Published on 13 Dec 2019 - 10:12

score 262 · Answer 15 · 2019-12-17 08:37:05

262

Views

$x\mapsto \frac{1}{1+x^2}$ is analytic

Published on 17 Dec 2019 - 8:37

List Question

An entire and one-to-one function must be of the form AZ+B, A non-zero. How to rule out higher degree polynomials in z?

Proof of the Riesz-Schauder Theorem (for compact operators) using the Analytical Fredholm Theorem

Sequence of partial sums converges locally uniformly?

Dimension of the solution space of a real analytic system of equations

PDE System and Analytic Functions

PDE Analytic System

A paradox on real vs complex analyticity

$f,g$ analytic on $I\subset \mathbb{R}$. If exist $a\in I$ such that $f=g$ and $f^{(n)}=g^{(n)}$then we have $f(x)=g(x)$ for every $x \in I$.

Real analyticity of harmonic functions

Analytical functions equal at a point implies all derivatives are also equal at that point?

Writing $f(x)=h(x)\cdot(x-\alpha)^m$ when $\alpha$ is a root of multiplicity $m$

Analytic maps from upper half plane to itself

Does here exists an analytic function $f:\mathbb C → \mathbb C$ such that $f(0) = 1, f(4i) = i$...

$J(z)= \frac{1}{\pi} \int _0 ^\infty \frac{z}{\eta^2+z^2} \ln (\frac{1}{1-e^{-2\pi \eta}}) d \eta$ is analytic in Re $(z)>0$

$x\mapsto \frac{1}{1+x^2}$ is analytic

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