- Docente: Loredana Lanzani
- Credits: 6
- SSD: MAT/05
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 23, 2023 to May 26, 2023
Learning outcomes
At the end of the course, the student has a knowledge of some basic features and methods of real and harmonic analysis.
Course contents
Topics covered include: Interpolation of Lebesgue spaces; Fourier coefficients; Hilbert and Riesz transforms; homogeneous singular integrals; Calderon-Zygmund decompositions. Time permitting, vector-valued singular integrals.
Readings/Bibliography
We will use the following textbook:
Loukas Grafakos, ``Classical Fourier Analysis'', 3d Edition (2014), Springer Graduate Texts in Mathematics v. 249.
Teaching methods
In-class lectures on the theory along with exercises, examples and applications, also aimed to students in the applied curriculum.
This course is taught in English; however students enrolled in the regular master program (not the international master) may choose to take the oral exam in Italian. During class, students who wish to ask a question may choose to do so in Italian.
Assessment methods
The evaluation is based on an oral examination that starts with the discussion of a topic chosen by the student among the topics covered during the course. The student will then answer questions pertaining to the proof of theorems that were demonstrated during lecture; the solution of exercises shown in class by the professor, or assigned by the professor as practice problems; the discussion of examples shown in class by the professor, or assigned by the professor as supplemental reading.
Students may choose to take the oral exam in Italian.
Teaching tools
Prerequisites for this course includes the following topics, which were covered in the ``Analisi Superiore'' component of the ``ANALISI SUPERIORE E GEOMETRIA DIFFERENZIALE'' course taught by Prof. Lanzani in Fall 2021, and can be reviewed in the following chapters in the textbook: Section 2.2 (Schwartz class & Fourier Transform); Section 2.3 (Tempered Distributions); Section 2.4.1 (Distributions supported at a point).
Office hours
See the website of Loredana Lanzani