New:*More challenges posted in Exercises.*Problem set 3 is posted in Exercises. It is due by 18/May/2018. 
»  
Course detailsThe contents are included in the guía docente.The lectures are scheduled on Monday and Wednesday 5:30pm  19:00pm in room 320 (Building 17, Science Faculty, Mathematics). For general reference, please check the master program website in the Department of Mathematics. 

»  
NotesI shall post periodically notes on the topics of the course. If you print them, please, note the possible page overlapping between the end of a section and the beginning of the next one.
The bibliography will be updated from time to time. Some of the topics in the previous list might not be covered in the course if time does not permit. I intend to write the corresponding notes anyway. Corrections and comments are welcome. Errata:  p.2, l.9. y_p=Ge^{i\omega_e t}  p.11, l.3. N\to\infty  p.7, (1.23). Missing L^{1} in the RHS.  p.49, (2.23). Extra 2 exponent.  p.49, (2.24). The denominator in the formula for a_j is without x.  p.50, formula fo L_k after (2.25) the factors of the product should be (xx_j)/(x_kx_j).  p.55, (2.44). In the ranges t and t should be x and y  p.57, (2.47). Adding a number to a matrix means adding it to each entry.  p.57, (2.48). The second matrix is M_2.  p.77. Change the title of 3.1.1 to "Windowed transforms".  p.78, (3.7). Extra hat in w.  p.82, (3.21). Missing da.  p.83. Missing "Suggested readings".  p.85, after (3.40) is = \phi(x)\phi(x1)  p.88, p.93. Include references to [GG12] and [Her17].  p.89 Th 3.1.9. "be such that {\phi ... }_{k\in\Z} is orthonormal" (missing end of the sentence).  p.89, 2^{j/2} in (3.65) and 2^{j} in (3.66) (the sign of the exponent is positive).  p.90, (3.72) second parenthesis should be big. Material and results of some of the in class experiments:


»  
ExercisesThe following sheets are home assignments that contribute to the grading.
Note: In the firstly posted version of Problem set 1, in the third line of 5) there was a missing absolute value (this is forced because the functions are even). It should read x\not\in [...,...]. The integral of f_\delta is 2 instead of 1. I have posted a corrected version. I am very sorry for the inconvenience. Note:In the first problem of Problem set 2, with "smooth" I assume that it decays as quick as you want, otherwise its Fourier transform could not exist or not being regular. The grades for officially enrolled students can be checked in the Moodle server after the home assignments are corrected. As mentioned below, a 25% of the grade can be got with (non mandatory) extra activities. From time to time some items will be added to the following list. The plan is to propose around 12 extra activities or so. A student completing 3 of them, not all theoretical, will get the full 25%. More than 3 activities increase the global grade. The number preceding each activity indicates approximately the chapter in the lecture notes it is related to.


»  
GradingThe grading is as follows: 1) Home assignments 75%.
2) Final exam* or extra
activities
25%.
For extra activities, see Exercises. *According with the information "Decanato" sent me, the final exam is scheduled at 01.17.SS.320 in 18/May/2018. Please check this information if you are willing to attend. 

LinksGeneral:
