Mathematics Stack Exchange
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Questions tagged [analysis]

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

Mathematical analysis is the rigorous version of calculus. In fact, it investigates the theorems in calculus with enough care and deals with them more deeply, trying to generalize the ideas in calculus. You can consider a more specific tag instead: , , , , , , etc. For data analysis, use .

42884 questions
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Uniform Continuity of non-Lipschitz functions

Ok so I have figured out it is differentiable over the reals and its derivative is unbounded, now I'm not too sure whether this is uniformly continuous on the reals, I can use the lipschitz property and it seems like it isn't but I could be wrong.…
Raul
  • 938
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Example involving Uniform Continuity

Question: Could someone give an example of a sequence of uniformly continuous real-valued functions on the reals such that they converge point-wise to a function that is continuous but not uniform continuous. My attempt so far: I managed to prove…
WhizKid
  • 857
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Derivatives of integration over level sets of a function

I want to take derivatives of the function given by the integral: $$ \int_{\{x\in\mathbb{R}^n: f=t\}}g(x)dx $$ with respect to t. Someone told me there is a proposition in manifold and geometry that such kind of derivatives have something to do with…
Xuxu
  • 1,174
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Analysis- convergence of functions pointwise problem

Ok I HAVE COMPLETED THE FIRST PART, however for the second part with the restriction on fn(x) I cant find a sequence of functions (I can find a sequence of functions but the integral does converge to 0 unfortunately), im guessing after thinking…
WhizKid
  • 857
2
votes
1 answer

Problem with a set without accumulation points

Let $S$ be a nonempty subset in $\mathbb R^m$ without accumulation points in $\mathbb R^m$. Is then $$ \inf \{ \|x-y\|: x,y \in S, x\neq y \} >0 \textrm{ ? } $$
user111
  • 447
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How Find this $f(x,y)$ such $f''_{xy}$ is not exsit.but $f_{xx}'',f_{yy}''$ is exsit.

Question: take example:such $f(x,y)$ in the unit disc $ D$ that extends continuously to ∂D such that $f_{xx}'',f''_{yy}$ exist,and continuously,But $f''_{xy}(0,0)$ is not exsit. My try: I have consider sometimes,and I can't looking for this…
user94270
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Can I use sequential continuity for one sided limits?

First of all sorry if this has been posted before, I had look but couldn't find anything thats exactly like my question. Suggest I am given a function $f[a,b] \rightarrow \mathbb{R} $that is regulated, Then I know that at any given point its has a…
user89921
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3 answers

Are there any whacky orderings of R?

Is there any way to reorder R so that 3 < 2? And a similar question, which probably can be answered in the same breath: Is d(2, 3) < d(2, 100) for all metrics? Is there a nice theorem that talks about this?
Julian Cienfuegos
  • 194
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2 answers

Limit goes to infinity, show that the f has a finite minimum.

So limit goes to infinity, and I have to show that there exists a finite infimum. how do i show this?
Dafty
  • 509
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1 answer

For any open subset $A\subseteq \mathbb{R}$, $\operatorname{int}(\overline{A})=A$?

In the quiz of a class in MIT OCW, there is a T/F problem : For any open subset $A \subseteq \mathbb{R}$, $\operatorname{int}(\overline{A})=A$? The hompage of the class also provided a answer, and I saw the answer of the above. The answer is False,…
NNNN
  • 1,495
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how to show that $A(x)\nabla u\in L_\mathrm{loc}^{2}(\Omega) $ for $u\in H_\mathrm{loc}^{1}(\Omega)$

Let $\Omega\subset \mathbb{R}^n$ be a connected open set containing $0$, $u\in H_\mathrm{loc}^{1}(\Omega)$, $A(x)\leq C|x|^{-1+\epsilon}$, where $\epsilon$ is small, and we also have $$ \|\nabla u\|_{L^2(|x|\leq R)}\leq C_{N}R^N,~~R\to 0, $$ for all…
Tomas
  • 1,369
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Uniform closure of an algebra $\Rightarrow$ uniformly closed algebra

In PMA, Rudin's book, there is the following theorem (7.29): Let $B$ be the uniform closure of an algebra $A$ of bounded functions. (Here, an algebra means a family of function satisfying that it is closed under addition, multiplication, and scalar…
NNNN
  • 1,495
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Is $||f||_p$ continuous in $p$

I just started learning about $L^p$ spaces today and I have this question: Let $(X,\scr{M},\mu)$ be a measure space. Let $f:X\rightarrow \mathbb{C}$ be measurable. Consider $\eta:]0,\infty[\rightarrow[0,\infty]$ that sends $p$ to $||f||_p$. Is…
Amr
  • 20,030
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Show that $f: GL_{n}(\Bbb R) \to GL_n \Bbb (R): A \mapsto A^{-1}$ is infinitely differentiable

Consider the continuous image $f: GL_{n}(\Bbb R) \to GL_n \Bbb (R): A \mapsto A^{-1}$ I'm trying to proof with induction that $f$ is infinitely differentiable. I now understand how I can proof that $f$ is one time differentiable. I found that $Df(G)…
Kasper
  • 13,528
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2 answers

Iteration of an operator

Let $f_0(x)$ be integrable on $[0,1]$, and $f_0(x)>0$. We define $f_n$ iteratively by $$f_n(x)=\sqrt{\int_0^x f_{n-1}(t)dt}$$ The question is, what is $\lim_{n\to\infty} f_n(x)$? The fix point for operator $\sqrt{\int_0^x\cdot dt}$ is…
Golbez
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