Recent content by sarrah1

Thank you very much Dan (first of all, all constants a,b,c,k are positive). I am trying to obtain bound (inequality) for Mittag-Leffler function E and I am about to reach this bound however except by imposing some restriction on the mittag leffler parameters. What I did is that I replaced the...

I forgot to say that a,b,c,k are all constants

Dear Colleagues I hope this post belongs here in calculus. It concerns a finite series for which I am seeking the sum. I tried using MATHEMATICA which didn't accept it. Perhaps if someone has Maple or any other software who can do it. Here it is attached. I shall be most grateful

I am extremely grateful Sarrah

Hello Simple question Whether the minimum of the product of two functions in one single variable, is it greater or less than the product of their minimum thanks Sarrah

I don't know how to thank you for your extreme help and time spent to help me out. You are a kind person Also for Oplag I am grateful to him he helped me in another situation. God bless you both. Sarrah

No I am extremely embarassed, I recalculated the singular values of the first matrix it is huge. Because I doubted it since I know that the spectral radius must be less than the spectral norm. What I was really looking for is either 1. A real matrix with large norm 1 or infinity but small...

Hello Klaas Sorry to have wasted your time Klaas. I know that the spectral norm of a real symmetric matrix is equal to its spectral radius. Meaning that the spectral norm is the smallest of all norms since the spectral radius is less than ||A|| (one or infinity or frobenius, etc..) So perhaps I...

Dear Klaas I am grateful for taking my question yet the matrix you gave is not real symmetric. My question is whether one knows of a real symmetric matrix with big norm and small eigenvalues OR a real matrix only like the one you wrote but having small singular values. Your matrix has big...

Hello Colleagues We know that for any square matrix | Lambda(A) | < ||A|| . I was looking for a matrix whether real symmetric with a large norm but small spectral radius or a general real matrix again with a large norm but small singular values. Any example will do, n up to 5 grateful thanks...

thank you very much

Hi colleagues This is a very very simple question I can show when $f$ is integrable and is even i.e. $f(-x)=f(x)$ then $\int_{-a}^{a} \,f(x)\,dx=2\int_{0}^{a} \,f(x)\,dx$ what about improper integrals of even functions, like the function ${x}^{2}\ln\left| x...

Hello A simple question. I have a linear integral operator (self-adjoint) $$(Kx)(t)=\int_{a}^{b} \, k(t,s)\,x(s)\,ds$$ where $k$ is the kernel. Can I say that its norm (I believe in $L^2$) equals the spectral radius of $K?$ Thanks! Sarah

Hi Oplag Upon reading your post again, and your easy and sound proof, it seems to me there is no such necessary condition, only a sufficient one. Perhaps I didn't express myself well. I meant convergence is guaranteed if $|\lambda|\rho(K)<1$ ok, which is tight but could it be that $|\lambda|...

I am most grateful Opalg. Eq. (3) can -as you did - be written of course as ${\varPsi}_{n}(x)-{\varPsi}(x)={\lambda}^{n}K^n({\varPsi}_{0}(s)-{\varPsi}(s))$ from which Eq. (4) also follows correctly The problem is - as it seems - from me. What I understood from your proof is that the...