Real and Complex Analysis

1. Front Matter

   Pages i-ix

   PDF

2. Lebesgue Integration

   • Rajnikant Sinha

   Pages 1-236

3. L^p-Spaces

   • Rajnikant Sinha

   Pages 237-390

4. Fourier Transforms

   • Rajnikant Sinha

   Pages 391-635

5. Back Matter

   Pages 637-637

   PDF

This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.

• Conformal Mapping
• Harmonic Functions
• Holomorphic Functions
• Fourier Transforms
• Lebesgue Integration

“This introductory book should be useful to undergraduate students in mathematics and engineering. … The approach to each topic appears to have been carefully thought out, both as to the mathematical treatment and to the pedagogical presentation. The end result is a quite satisfactory book for undergraduate classroom use or even self-study.” (Christian Lavault, Mathematical Reviews, July, 2019)

• Varanasi, India

  Rajnikant Sinha

RAJNIKANT SINHA is former professor of mathematics at Magadh University, Bodh Gaya, India. A passionate mathematician, Prof. Sinha has published numerous interesting research findings in international journals and books, including Smooth Manifolds (Springer) and the contributed book Solutions to Weatherburn’s Elementary Vector Analysis. His research focuses on topological vector spaces, differential geometry and manifolds.

Policies and ethics