Recent content by Zaare

I think you're correct in your assumption, LeonhardEuler, since the problem is: "Fourier series: Find the coefficient". So I assume they only want the coefficient of the sin terms. Thank you for the help. And, lurflurf, thanks for the explanation about the limits.

I'm somewhat confused about how to find this particular Fourier coefficient. Let me explain: I have these two formulas from the book: (1) \qquad f\left(x\right) = \frac{a_0}{2}+\sum_{n=1}^\infty\left[a_n cos\left(n \Omega x\right)+b_n sin\left(n \Omega x \right)\right], \quad \Omega =...

Oh, right, so k must be an even integer. Thank you. :smile:

I don't know how to use the extra condition given in the this problem: f^{\prime\prime}+\lambda f = 0, f=f\left(r\right) f\left(r\right) = f\left(r+\pi\right) For \lambda = 0, the solution is some constant. For other \lambda, I put \lambda=k^2, and get f^{\prime\prime}+k^2 f =...

Finally, I solved this a couple of days ago. Schmoe, I followed your "recipe". It was of great help. Thank you all.

I'm stuck trying to solve the following problem: If D_n is the Dirichlet kernel, show that there exist positive constants c_1 and c_2 such that c_1 \log n \le \int\limits_{ - \pi }^\pi {\left| {D_n \left( t \right)} \right|dt} \le c_2 \log n , for n=2,3,4,.... By \log they mean the...

Ok, here's the way I reason: In (a) I showed that the Fourier coefficient has an upper limit. Then in (b) I showed that a certain function satisfying the desired condition has a Fourier coefficient which is of the same size as the upper limit in (a). Then obviously the upper limit cannot be...

I need help with the last part of the following problem: Let f(x) be a 2\pi-periodic and Riemann integrable on [-\pi,\pi]. (a) Assuming f(x) satisfies the Hölder condition of order \alpha \left| {f\left( {x + h} \right) - f\left( x \right)} \right| \le C\left| h \right|^\alpha , for...

Ok, here's my reasoning. The integrand f(x+\frac{\pi}{n})e^{-inx} is 2\pi-periodic. Hence a change from x+\frac{\pi}{n} to x+\frac{\pi}{n}+2\pi leaves the integrand unchanged and I get \int\limits_{ - \pi }^{ - \pi + {\pi \mathord{\left/ {\vphantom {\pi n}} \right...

I'm supposed to show \hat f\left( n \right) = - \frac{1}{{2\pi }}\int\limits_{ - \pi }^\pi {f\left( {x + {\pi \mathord{\left/ {\vphantom {\pi n}} \right. \kern-\nulldelimiterspace} n}} \right)e^{ - inx} dx} where \hat f\left( n \right) is the Fourier coefficient and f(x) is a...

First the problem: If D_n is the Dirichlet kernel, I need to show that there exist positive constants c_1 and c_2 such that c_1 \log n \le \int\limits_{ - \pi }^\pi {\left| {D_n \left( t \right)} \right|dt} \le c_2 \log n for n=2,3,4,.... The only thing I have been able to do is this...

Yes, and if it's not cyclic: Is it "at least" abelian? I'm sorry about the poor specification.

But a certain value of n defines a certain H, so I have to consider the different values n can take. What I mean is for any n.

I don't mean to treat n as a variable, only as an unknown constant. Where do I treat it as a variable?

Since G is a finite group, then every element in G must equal identity for some n. That means that for some n the element must be added to H. So I think the answer is no. But I can't make any connection to my problem. If I haven't made any mistakes, it has 2 elements of order 3 and 3 elements...