Titlebook: Real and Complex Analysis; Volume 1 Rajnikant Sinha Textbook 2018 Springer Nature Singapore Pte Ltd. 2018 Conformal Mapping.Harmonic Functi

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Lebesgue Integration,Inadequacies of the Riemann integration, and difficulties in handling limit processes in it were largely overcome with the advent of abstract integration.

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Fourier Transforms,In this chapter, we introduce total variation, and prove the Radon-Nikodym theorem. The Fubini theorem and change-of-variable theorem are also proved. Finally, we prove the Plancherel theorem on Fourier transforms.

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https://doi.org/10.1007/978-981-13-0938-0Conformal Mapping; Harmonic Functions; Holomorphic Functions; Fourier Transforms; Lebesgue Integration

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