Real Analysis II

  • 申立勇
  • Created: 2014-12-08
Real Analysis II

 

Course No.S070101ZJ009 

Course Category  Professional Basic Course      

Period/Credits40/2

PrerequisitesMathematical analysis, Real variable functions, Functional analysis, General topology.

Aims & Requirements

The curriculum is a core course for both the postgraduates and the doctorates from all fields of mathematics and also an elective course for graduates who major in theoretical physics. The main contents of the course include basic operator theory, Fourier analysis on Euclidean spaces, the generalized function theory, Hardy spaces Hp and BMO spaces. Through learning the course, the students can master the basic concepts, methods, skills of modern real analysis and lay foundation for further studying modern mathematics and doing further research work in mathematics.

Primary Coverage

Chapter 1  Basic operator theory 

Convolution operators; HardyLittlewood maximal operators; Identity approximation operators; Interpolation theorem.

Chapter 2   Fourier analysis on Euclidean spaces

The basic  theory of the Fourier transform; The  theory of the Fourier transform.

Chapter 3  Generalized function theory

The Schwartz function spaces; Generalized function spaces.

Chapter 4   Hardy spaces Hp and BMO spaces

Hardy spaces Hp and BMO spaces; Calderon-Zygmund theory.

 

Textbooks

1.  Walter Rudin, Real and complex Analysis, Third Edition. 

2.  Anthony W. Knapp, Advanced Real Analysis, Birkhauser Boston Basel Berlin,  2005

References

1.      E. M. Stein, R. Shakarchi, Real Analysis  World Scientific,  2006.

2.      R. L. Wheeden and A. Zygmund, Measure and Integral, 1977.

 

Author::Dunyan YanMathematical Science, GUCAS                          

Date November, 2011.