Weekly outline

  • About this web page

    The class web page is at https://eigen-space.org/mk/harmonic1920/. It continues to be updated with new material.

    This moodle page was created after the course moved online (mid March 2020, because of the coronavirus situation). It serves as a host for the class discussion forum (which everyone is encouraged to use, preferably in English, but also in Greek if you cannot express yourself in English with ease).

    It is also here where you will be uploading your assignments (solutions to problem sets).

    How to upload your solutions to problem sets

    For each assignment you should upload one PDF file. No images, no word files, no multiple files.

    Most of you will be writing your solutions on paper (of course, latex produced files are very welcome). I suggest you do the following after you have written your solutions as clearly as you can.

    Use a phone app such as Camscanner or Tiny Scanner to scan the pages into one pdf file (it is very important to have good light when you take the pictures -- natural light works best). This you upload to your assignment before the due date.

  • 22 March - 28 March

    • Problem set No 10 Assignment

      Problem set No 10, in English and Greek. On equidistribution and Weyl's theorem. Refer to the web page of the class for the corresponding material.

      Due March 31, 2020. Upload your pdf here.

    • Problem set No 11 Assignment

      Problem set No 11, in English and Greek.  On the construction of a continous function which is  nowhere differentiable. Refer to the web page of the class for the corresponding material.

      Due April 7, 2020. Upload your pdf here.

  • 29 March - 4 April

    • Problem set No 12 Assignment

      Problem set No 12, in English and Greek.  On the proof of the Weierstrass approximation theorem due to Bernstein. Refer to the web page of the class for the corresponding material.

      Due April 14, 2020. Upload your pdf here.

    • Problem set No 13 Assignment

      Problem set No 13, in English and Greek.  On the \(L^2\) theory of Fourier series. Refer to the web page of the class for the corresponding material.

      Due April 27, 2020. Upload your pdf here.

  • 12 April - 18 April

    • Problem set No 14 Assignment

      Problem set No 14, in English and Greek.  Elements of functional analysis, the Banach-Steinhaus theorem and failure of convergence of the Fourier series for a continuous function. Refer to the web page of the class for the corresponding material.

      Due May 4, 2020. Upload your pdf here.

  • 26 April - 2 May

    • Problem set No 15 Assignment

      Problem set No 15, in English and Greek.  Convergence of the partial sums in various norms. Criteria for convergence at a point (Dini, Hardy). Refer to the web page of the class for the corresponding material.

      Due May 11, 2020. Upload your pdf here.

  • 3 May - 9 May

    • Problem set No 16 Assignment

      Problem set No 16, in English and Greek.  Convergence of the partial sums in various norms. Criteria for convergence at a point (Dini, Hardy). Refer to the web page of the class for the corresponding material.

      Due May 20, 2020. Upload your pdf here.

  • 17 May - 23 May

    • Problem set No 17 Assignment

      Problem set No 17, in English and Greek.  Convergence of the partial sums in various norms. Criteria for convergence at a point (Dini, Hardy). Refer to the web page of the class for the corresponding material.

      Due May 31, 2020. Upload your pdf here.

  • 21 June - 27 June

    • Final exam: Tue, 23 June, 2020, 14:00-16:00. Exam in class, not online.