Recent content by naaa00

Hi there, I'm actually trying to understand why the behaviour of the Gamma function at z = -n is (-1)^n/(n!z) + O(1) The first term (although without the z) I recognized it as the residue of f when z= -n. But the rest, no idea. Any explanation is very appreciated.

Homework Statement Hello, H is a Hilbert space. K is a nonempty, convex, closed subset of H. Prove that the orthogonal projection Pk: H → H, is non-expansive: ll Pk(x) - Pk(y) ll ≤ ll x - y ll The Attempt at a Solution So the length between the Pk's, which is in K (convex) is less than...

The LaTex code is not working, apparently... Really difficult to figure out what you wrote.

Do you have Rudin's "Principles of mathematical analysis" 3th edition? Rudin's definition of the partials is on pag. 215. And the complete proof of the part avobe is on pag. 219. The scalar product isn't supposed to be the product of two equal length sequences of numbers?

Hello Voko, Thanks for the answer. That's a part of the proof that shows that a map is continuous differentiable iff the partials exist and are continuous on E. The " D_j f_i " correspond to the partials. I'm still not sure about the last term. What I'm thinking is that f'(x) and f'(y) are...

Homework Statement Hello, I'm little bit confused about a particular inequality in a proof: | (D_j f_i) (y) - (D_j f_i) (x) | ≤ | [(f'(y) - f'(x)]e_j | ≤ ||f'(y) - f'(x)|| The last part of the inequality confuses me. Is the absolute value (norm on R) less than any other norm on R^n?

Homework Statement Hello, I'm trying to find the Taylor representation of a product of functions - the exponential of x times sin(y). Also for (x - y)sin(x+y). The Attempt at a Solution Well, I want to use the Cauchy product in both cases. I know the taylor representation of both...

Hello Halls, The one in the middle.

I see! Really interesting - I actually didn't saw the exponent and the (1/x) inside the parenthesis (for the particular case, e) as to independent functions...

I just realize that I didn't consider the limits of integration... The limits are from 0 to infinity... but still something must be wrong...

Hello Infinitum, I have never heard of this. Does it has a particular name? I'm trying to look on the internet, but I don't find anything related to that. Do you have a link that you could share?

Homework Statement R(x) := ∫ exp ( -y^2 - x^2/y^2 ) dy The Attempt at a Solution I move the derivative operator inside the integral and differentiate with respect to x R'(x) = ∫ [ - 2x/y^2 ] exp ( -x^2/y^2 - y^2 ) dy Then I let: t = x/y and dy = - x/t^2 dt R'(x) = 2 ∫ [ - x ] [ t^2 /...

Thanks. I’ll try to be more aware with the meaning of each part of a definition. But I’m still not sure what’s going on. The definition says that the L_op is defined as the min M such that the norm of L(x) on R for all x is less or equal than this M times the p-norm on R^n. So the length of...

Hello. Thanks for your answer! Well, I applied Hölder's inequality. Then I found that the p-norm of L times the p-norm of 1 is bigger than L. Then by the definition of the operator norm, I can say that the right hand of the inequality is indeed the operator norm?

Homework Statement L : R^n → R is defined L(x1 , . . . , xn ) = sum (xj) from j=1 to n. The problem statement asks me to find an estimation for the operation norm of L, where on R the norm ll . llp, 1 ≤ p ≤ ∞, is used and on R the absolute value.The Attempt at a Solution from, ll Lv lly ≤...