Theory of functions of a real variable
(Complete Item Description)
- Abstract:
I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications. In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for compact self-adjoint operators and applications of this theorem to elliptic partial di erential equations. Chapter III is a rapid presentation of the basics about the Fourier transform. Chapter IV is concerned with measure theory.
- Subject:
- Mathematics and Statistics
- Grade Level:
- Post-secondary
- Collection:
- Harvard University