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Results tagged with ca.classical-analysis-and-odes
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user 4606
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
-6
votes
1
answer
432
views
On the extension of a limit [closed]
We know that $\lim_{p\rightarrow\infty}\left\Vert \left(x_{1},\cdots,x_{n}\right)\right\Vert _{p}=\max\left\{ \left|x_{1}\right|,\cdots,\left|x_{n}\right|\right\} =:\left\Vert x\right\Vert _{\infty}$
…
- 65
1
vote
2
answers
395
views
Are there always nontrivial real solutions to $A_1 x^5 + B_1 y^5 + C_1 z^5 = 0$ and $A_2 x +...
Firstly, are there always nontrivial real solutions to the sysytem
of equations, $A_{1}x^{5}+B_{1}y^{5}+C_{1}z^{5}=0$ and $A_{2}x+B_{2}y+C_{2}z=0$,
for real numbers $A_{1}$, $B_{1}$, $C_{1}$, $A_{2}$, …
- 65
0
votes
1
answer
357
views
Questions on supremum
Is it true that $$\sup_{x\in\mathbb{R}}\frac{\left|\left(1+s\right)+tx\right|+\left|\left(1+t\right)x+s\right|}{1+\left|x\right|+\left|s+tx\right|}\geq1$$
for all $s,t\in\mathbb{R}$? Is it also true t …
- 65
-3
votes
2
answers
260
views
On \ell_3 norm in R^2
Let $v,w\in\mathbb{R}^{2}$ and $v\perp w$. Is it true that $\left\Vert v\right\Vert _{3}\leq\left\Vert v+w\right\Vert _{3}$,
in which $\left\Vert \left(x,y\right)\right\Vert _{3}:=\sqrt[3]{\left|x\rig …
- 65