Master's Thesis

Tuesday, April 18. 2006

Yahoo, 26 hours!

This touches my project only at the margin, but my employer agreed to reduce my working hours to 26/week! It was my psychologically motivated target to be able to leave the office at 15:00h if I start working at 8:00h. As I sometimes might begin later and might have to stay a little longer if needed, the leaving time will often get postponed anyway.

The change of my employment contract leads to a “restart at zero”, i.e., all unused holidays and accumulated overtime will get paid off, which isn’t such a benefit for me. However, I have reached a milestone. If I really want to stay in my time plan, I’ll have to do 5 pages/day in Blatter as well as in Gröchenig, and this is only possible if I have enough time available. And there is much more literature.

Posted by Stephan Paukner in Master's Thesis at 17:23 | Comments (0) | Trackbacks (0)

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Monday, April 17. 2006

Time plan until June

Until the mid of May, i.e. in one month, I want to have finished reading the Wavelet Primer and the whole functional analysis, including the script of Prof. Cigler. Until the end of May, I want to fix the topic of my thesis. Until the end of June, I want to have finished reading the Foundations of Time-Frequency Analysis; the two weeks of holiday at the beginning of June are already taken into account. After my holidays, i.e. by the mid of June, I definitely want to start on my special topic.

One of my next steps is to check out if sampling theory could be the topic of choice. I stepped over the book Sampling, Wavelets and Tomography, which appeared quite interesting to me. The NuHAG library owns it, but it is currently borrowed by Tobias W. Karin’s CD includes his master thesis, among other papers, and I think I will ask him how I should proceed to get an overview and if he had an idea for a concrete topic. I will contact him after having read the brief summary of Shannon’s sampling theorem in Blatter’s Wavelet Primer, which I will reach within the next days. HGFei still hasn’t answered yet, and I don’t know what I should think about that.

Posted by Stephan Paukner in Master's Thesis at 18:56 | Comments (0) | Trackbacks (0)

Friday, April 14. 2006

Meeting at Karin

Yesterday I was at Karin’s flat to talk about mathematics, master thesis, master exam, and much more. She wants to take the master exam at the beginning of May. We had a little overview about the most important theorems in functional analysis. She gave me a CD containing all her TeX files, some papers and of course her own master thesis, which she had finished recently.

Posted by Stephan Paukner in Master's Thesis at 08:23 | Comments (0) | Trackbacks (0)

Wednesday, April 12. 2006

Starting with time-frequency analysis

I’ve finally done chapter VII of Werner’s book. At the end of that chapter, I didn’t follow the content in detail anymore, as it appeared more and more exotic to me and not too much related to TF-analysis. The two remaining chapters (Locally convex spaces incl. distribution theory, Banach algebras) will be done within one or two months, but without force; it will be enough to go through 2 pages per day.

The main focus now should be time-frequency analysis, repeating basics about Hilbert spaces and Fourier- as well as wavelet-analysis. I’ve already started to read Gröchenig’s Foundations some time ago. Also, I finally bought Blatter’s Wavelet Primer in its German original.

I contaced HGFei and told him about my current status. I asked him whether I should try to fix a topic or if I should continue reading. Also, I told him about my idea of taking measure and integration theory for my master exam. He hasn’t answered yet.

Posted by Stephan Paukner in Master's Thesis at 07:09 | Comments (0) | Trackbacks (0)

Sunday, April 9. 2006

Inclusions of $L^p$-spaces

Just a note: We know that the inclusion $\ell^1\subseteq\ell^{p_1}\subset\ell^{p_2}\subseteq\ell^\infty$ yields for $1\leq p_1<p_2\leq\infty$ . A similar inclusion statement is valid for $L^p$ -spaces iff we look at $L^p[a,b]$ . Here, for $p_1<p_2$ , the inclusion is the other way round: $L^{p_2}\subset L^{p_1}\subseteq L^1$ . This is not valid for $L^p(\mathbb{R})$ , as $\int_{\mathbb{R}}dt$ is not finite. In Cigler’s script, the fact $L^{p_2}\subset L^{p_1}$ had just been written down quickly, and it wasn’t mentioned that this was only valid for bounded intervals. I already wondered why it was always said that the Fourier transform could be expanded to “ $L^2\cap L^1$ ” and not simply “ $L^2$ ”.

Posted by Stephan Paukner in Master's Thesis at 16:30 | Comments (0) | Trackbacks (0)

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Wednesday, April 5. 2006

Progress in functional analysis, III

I will start with spectral decomposition of self-adjoint operators today. It will take me about one week to go through that last chapter of my reading plan of this book, so I won’t be so far behind my original time plan.

I think I’ll have to buy Blatter’s Wavelet primer, as I start wanting to write notices into the borrowed copy. It provides an easily readable approach and isn’t that expensive.

Posted by Stephan Paukner in Master's Thesis at 08:08 | Comments (0) | Trackbacks (0)

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