## Complex Analysis |

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which
- Japanese
- Beijing Lectures in Harmonic Analysis. (AM-112). [Paperback]
- Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11). [Paperback]
- Fourier Analysis: An Introduction. [Hardcover]
- Functional Analysis: Introduction to Further Topics in Analysis. [Hardcover]
- Hardy Spaces on Homogeneous Groups. (MN-28). [Paperback]
- Harmonic Analysis (PMS-43): Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43). [Hardcover]
- Introduction to Fourier Analysis on Euclidean Spaces (PMS-32). [Hardcover]
- Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems. (MN-24). [Paperback]
- Real Analysis: Measure Theory, Integration, and Hilbert Spaces. [Hardcover]
- Singular Integrals and Differentiability Properties of Functions (PMS-30). [Hardcover]
- Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63). [Paperback]
- Fourier Analysis: An Introduction. [Hardcover]
- Functional Analysis: Introduction to Further Topics in Analysis. [Hardcover]
- Real Analysis: Measure Theory, Integration, and Hilbert Spaces. [Hardcover]
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