Recent content by LikeMath

If the derivative is increasing that mean the original function is concave up, but how can that solve the question. I did not get it.

Hi! I have the following question. Let f be continuous on [0,\infty[, f(0)=0, f^\prime exists on ]0,\infty[, and f^\prime is increasing on ]0,\infty[. the question is to prove that the following function is increasing that is g(x)=f(x)/x on ]0,\infty[. I tried to show that the first...

thank you very much

Hey there, Does the set (z^n ; n\in N) span L^2[0,1]? Thanks in advance

Thank you, but how can I convince my self that it is doable?

Hi there, I am reading an article, but I faced the following problem, and I am wondering if it is well known fact. If the integral of a function on some interval is infinity, can we partition this interval into countable disjoint (in their interiors) subintervals such that the integral...

Hey! Is there an infinite ring with exactly two maximal ideals. Thanks in advance LiKeMath

Let f(z)=z+\frac{1}{z}, the question is to find the image of this function on |z|>1. To do so, I tried to find the image of the unit circle which is the interval [-2,2] and so I could not determine our image. If also we tried to find the image of f we get f(re^{i\theta})=u+iv where...

Any idea?

Hi, Let H^2 be the Hardy space on the open unit disk. I am wondering how can I compute the following inner product <\frac{1}{\left(1-\overline{\alpha_1} z\right)^2}\frac{z-\alpha_2}{1-\overline{\alpha_2} z},\frac{z}{\left(1-\overline{\alpha_1} z\right)^2}>, where \alpha_1,\alpha_2 in the unit...

Ok, but the basis in your example is linearly independent in the finite sense, is not it? By the way are you really a high school student? Thx

Ah ok, now I understand your point. In my question I mean Schauder basis (not the Hamel basis). Thank you for drawing my attention to this piont.

That is every member of E can be written in a uniquely linear combination of vectors from this basis. I wonder if it "basis" has another definition?

Hi there! A Hilbert space E is spanned by a set S if E is generated by the element of S. It is well known that in the finite dimensional case that S spans E and S is linearly independent set iff the set S form a basis for E. The question is that true for the infinite dimensional...

Yes you are right, "easy" was not appropriate.