Movatterモバイル変換

Question 1

1vote

0answers

32views

Suppose $D^3f$ exists, prove $D_AD_AD_A f$ exists.

Let $A,B,C$ be (banach) normed spaces. On $A\times B$ we consider the supremum norm. Let $X\subseteq A \times B$ be an open set.Let $f: X \rightarrow C$ and suppose its third differential map exists,...

Cezar

157

askedyesterday

Question 2

0votes

0answers

23views

Intuition connecting the definition of norm of a number with its p-adic expansion

Let $\alpha\in K$ where $K$ is an algebraic extension of $\mathbb{Q}_p$ and $n:= [K : \mathbb{Q}_p]$.Let $f(x) : = x^n + a_{n-1}x^{n-1}+...a_0$ be a minimum polynomial of $\alpha$ over $\mathbb{Q}_p$....

emmy

256

asked2 days ago

Question 3

0votes

1answer

113views

Using self-adjoint operator to define Euclidean norm

I am trying to understand definition of Euclidean norm on a finite dimensional space, $\mathbb{R}^{n}$, denoted as $\mathbb{E}$. The dual space is denoted by $\mathbb{E}^{*}$.In the attached ...

jayant

143

askedNov 25 at 21:40

Question 4

0votes

0answers

86views

A characterization of norms coming from inner products

Let $X$ be a normed vector space and fix two distinct vectors $u$ and $v$ in $X$. Consider the set: $E(u,v) = \{z\in X | |z-u| = |z-v|\}$.An interesting fact I observed is that if the norm that ...

Lizards

33

askedNov 24 at 11:04

Question 5

0votes

1answer

73views

Are all norms of complex fields spherical?

Any complex vector space $\mathbb{C}^{n}$ is isomorphic to a real vector space $\mathbb{R}^{2 n}$. I was wondering, however, if converting complex vector spaces to real ones offers more freedom with ...

Hippopotoman

3

askedNov 18 at 17:07

Question 6

4votes

1answer

59views

Remote generation of functions

The following problem appeared in my current quest for understanding fundamental physics. It is a bit complicated, but I try to explain it as clearly as possible. The problem has to do with the ...

flippiefanus

216

askedNov 18 at 10:01

Question 7

3votes

1answer

55views

Equivalency of a mixed Sobolev norm

I was working on a problem and the following question arose. Consider the norm$$ \| (-\Delta)^\gamma (1-\Delta)^{- \gamma /2} f\|_{L^2}.$$It appears to combine features of the usual inhomogeneous ...

N230899

401

askedNov 16 at 15:34

Question 8

0votes

0answers

54views

Schur's test with weight for infinite matrices and weighted $\ell^2$ spaces

I have come across Schur's test in the presentation here. It states the following.Let $A=(a_{ij})$ be an infinite complex matrix, $(p_n)$ and $(q_n)$ be two sequences of positive real numbers, and ...

Gergő Nagy

1

askedNov 7 at 7:47

Question 9

4votes

2answers

116views

How good is computing $\left\|f\right\|_p$ with large $p$ as a numerical approximation for $\left\|f\right\|_{\infty}$ for functions $f$?

Let's suppose that I wanted to compute $\left\|f\right\|_{\infty}=\sup_{t \in \mathcal{T}} \left|f(t)\right|$ for a $f$ that may not be easy to optimize. This is the infinity norm of a function, and ...

cgmil

1,553

askedOct 23 at 17:56

Question 10

1vote

1answer

75views

Sequence of vector units $x_1, x_2, \ldots$ in a normed space $X$ such that they are all linearly independent and their distances are $>1$.

I'm on my first semester of the Functional Analysis course that we have in my university. I've been stuck on this particular problem our professor presented to us not long ago for a while now:Let $...

Pabloo

121

askedOct 22 at 19:25

Question 11

5votes

1answer

226views

Motivation for Riesz' Lemma

I have known the Riesz' lemma for a long time. I know it is very important as it help characterise finite dimensional normed linear spaces. But its statement does not seem very natural to me. What can ...

MB123

61

askedOct 14 at 8:14

Question 12

0votes

0answers

60views

Uniqueness of extrema for convex functions in a normed space

The statement and the proof are taken from a real analysis book.Theorem: Let (V, ρ) be a normed space and $A$ be a convex subset of V. Considera concave (convex) function $f : A → \mathbb{R}$. Then,...

Giulio Lanza

53

askedOct 13 at 17:43

Question 13

0votes

0answers

34views

For normed vector space, can different norms make sequence to different limits? [duplicate]

A vector space can has different norms. A sequence can converge in a norm, but diverge in another norm. However, can there be:A vector space $V$Two norms $\left\| \cdot \right\|_1$, $\left\| \cdot \...

user1596524

1

askedOct 10 at 8:16

Question 14

1vote

1answer

100views

Question about an expression of the norm $\|A\|_{\infty\rightarrow 1}$

Given a matrix $A$, the norm $\|A\|_{\infty\rightarrow 1}$ is $\max_{x:\|x\|_{\infty}=1}\|Ax\|_1$.A reference says that$$\|A\|_{\infty\rightarrow 1}=\max \sum_{i,j}A_{ij}c_id_j,$$where the maximum ...

Connor

2,504

askedOct 7 at 21:58

Question 15

1vote

1answer

119views

Does the Mean Value Theorem work for differentiable functions $f:E\to \mathbb{R}$ defined on any normed space $E$?

It is know that if $f:\mathbb{R}^n\to \mathbb{R}$ is differentiable and $[a,b]$ is the segment from $a$ to $b$, there is at least one number $c\in [a,b]$ such that $df(c)(b-a)=f(b)-f(a)$. The proof ...

ted

316

askedOct 7 at 12:59

Movatterモバイル変換

Stack Exchange Network

Questions tagged [normed-spaces]

Suppose $D^3f$ exists, prove $D_AD_AD_A f$ exists.

Intuition connecting the definition of norm of a number with its p-adic expansion

Using self-adjoint operator to define Euclidean norm

A characterization of norms coming from inner products

Are all norms of complex fields spherical?

Remote generation of functions

Equivalency of a mixed Sobolev norm

Schur's test with weight for infinite matrices and weighted $\ell^2$ spaces

How good is computing $\left\|f\right\|_p$ with large $p$ as a numerical approximation for $\left\|f\right\|_{\infty}$ for functions $f$?

Sequence of vector units $x_1, x_2, \ldots$ in a normed space $X$ such that they are all linearly independent and their distances are $>1$.

Motivation for Riesz' Lemma

Uniqueness of extrema for convex functions in a normed space

For normed vector space, can different norms make sequence to different limits? [duplicate]

Question about an expression of the norm $\|A\|_{\infty\rightarrow 1}$

Does the Mean Value Theorem work for differentiable functions $f:E\to \mathbb{R}$ defined on any normed space $E$?

Hot Network Questions

Subscribe to RSS