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I'm interested in elementary introduction to pseduodifferential operators and its application to hyperbolic PDE's. I know measure theory, Fourier analysis and some elementary(linear) hyperbolic PDE's but not functional analysis, distributions, Sobolev spaces,etc. Can you recommend suitable intro text? Thanks

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There is of course Hörmander's magnum opus The Analysis of Linear Partial Differential Operators (Springer); pseudodifferential operators are discussed in volume III.

Less technical is Michael Taylor's book Pseudodifferential Operators (Princeton University Press). He also has a set of lecture notes and a pdf of his book Pseudodifferential Operators and Nonlinear PDEs (Birkhäuser) on his website.

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The easiest introduction is "An Introduction to Pseudo-differential Operators by "M. W. Wong". However it is not so general as Hörmander or Taylor. It develops the theory only for the classes $S^m_{1, 0}$. The requisites are very modest. Another nice reading is "Pseudo-differential and Singular Integral Operators" by "H. Abels".

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The best introduction is Raymond Elementary Introduction to the Theory of Pseudodifferential Operators CRC Press.

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