How to prove this density result?
Let’s learn how to prove this density result. The most accurate or helpful solution is served by Mathematics.
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Assume that $b\in \mathbb{C}$ such that $0<\vert b \vert <1$. We consider the familly $f_{p}=\{1,b^{p},b^{2p},b^{3p},b^{4p},...,b^{np},...)$. How can one prove that $\operatorname{Span}(f_{p}, \ p\in \mathbb{N}^{*})$ is dense in $l^{2}(\mathbb{C})$? Thanks.
Answer:
Assume that $x$ is orthogonal to each $f_p$. The function $$h(z):=\sum_{k=0}^\infty x_kz^k$$ is holomorphic...
jeffrey-c at Mathematics Mark as irrelevant Undo
Other solutions
What are some examples where a result is subconsciously obtained and there was certainty that the new result was correct. One famous example is from the French mathematician Henri Poincare. He wrote, “For fifteen days I strove to prove...
Answer:
Actually, pretty much any idea, mathematical or not, largely originates nonconsciously, both when you...
Yasha Berchenko-Kogan at Quora Mark as irrelevant Undo
I can't just say "raft is less dense then sea". How do I prove raft will float?
Answer:
show that the buoyant force on it will equal its weight the weight of the raft is 380kg/m^3 x 2.25m...
CXRJESXBAKZARWOLFPPGSH7DOE at Yahoo! Answers Mark as irrelevant Undo
South Zone have beaten West Zone in the Duleep Tropjy Final, by successfully chasing down 536 to win, the highest winning runchase in first-class history: http://www.cricinfo.com/duleeptrophy2009… The much maligned Yusuf Pathan was hero of the...
Answer:
Cricket is truly a funny game. Now it looks as if no total is safe. Even in ODIs, a total as high as...
▐►Supreme ▓ Sachin◄▌ at Yahoo! Answers Mark as irrelevant Undo
Lets say a Product Manager wants to trigger a 'sign-up' modal on every single page the user visits until they have signed up. This will almost certainly improve the sign up KPI, but it will be highly annoying to users. Since there is no way to tell specifically...
Answer:
You can try and infer certain things purely from data, but data doesn't always give you the full picture...
Josh Pigford at Quora Mark as irrelevant Undo
QUESTION: Hello, I have a specific question about PCM and TEM, but let me give you some background information first. We are having a bathroom addition put in this spring and builders ran into a small amount of old pipe insulation containing asbestos...
Answer:
PCM samples (or any type of air sample for that matter) can be collected 2 different ways, static or...
Miningco.com Mark as irrelevant Undo
From watching the motion of Charon around Pluto, we can measure its orbital radius and period, and then from Kepler's Law we can determine that Pluto is 0.002 times the mass of Earth. From timing the eclipses of Pluto by Charon we measure that Pluto...
Answer:
According to the search engine WolframAlpha, the density of Pluto is 2 grams per cubic centimeter. ...
Kelly at Yahoo! Answers Mark as irrelevant Undo
Doing a project for physics. Going to prove that the clip from "The Core", where they used laser/ultra sound blaster to make a tunnel through the rock couldn't happen. We are doing this by looking at the dust that the blast admits and sighting...
Answer:
Isn't it enough proof that whoever wrote this film must have been smoking something funny? If they even...
lord_eri... at Yahoo! Answers Mark as irrelevant Undo
For the past 10 years or so, my dad has bought me a lot of computers as that is my hobby. Anyway, most of them were given to me, and have always been mine. Now, that I'm an adult (22) my dad and I no longer live together because we had a major falling...
Answer:
Tell him to take you to court. The most he can get in civil claims court is like $5000 worth of stuff...
Matthew at Yahoo! Answers Mark as irrelevant Undo
I'd like to know the formula to find the density of any planet, inside our solar system. It is for a math project at my school in which I need to use integrals. I'm taking this initiative from a Nasa exercise called "The Internal Density and Mass...
Answer:
Why wouldn't you just divide the mass of the planet by its volume? Why do you need an integral? Is the...
Diego Orlando at Yahoo! Answers Mark as irrelevant Undo
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