From the reviews: "The book is devoted to explaining a close relationship between the pseudodifferential analysis and the well-known theory of automorphic functions and modular forms on the upper Poincare half-plane II, or their generalization as automorphic distributions. ... the book is perfectly readable and rich with analytic details for both researchers in pseudodifferential analysis and for number theorists." (Do Ngoc Diep, Mathematical Reviews, November, 2013) "In this book the author explains very beautiful links between pseudodifferential analysis and the theory of nonholomorphic modular forms on the classical modular group ... . The book is excellently written and represents an extremely valuable contribution for the two research communities - analysts from PDEs and pseudodifferential operators and number theorists. It exhibits a lot of new and original links between the two research areas. It is self-contained and easily accessible for a broad readership." (Soren Krausshar, Zentralblatt MATH, Vol. 1243, 2012)

• Introduction.- The Weyl calculus.- The Radon transformation and applications.- Automorphic functions and automorphic distributions.- A class of Poincaré series.- Spectral decomposition of the Poincaré summation process.- The totally radial Weyl calculus and arithmetic.- Should one generalize the Weyl calculus to an adelic setting?.- Index of notation.- Subject Index.- Bibliography.

From the reviews: "The book is devoted to explaining a close relationship between the pseudodifferential analysis and the well-known theory of automorphic functions and modular forms on the upper Poincare half-plane II, or their generalization as automorphic distributions. ... the book is perfectly readable and rich with analytic details for both researchers in pseudodifferential analysis and for number theorists." (Do Ngoc Diep, Mathematical Reviews, November, 2013) "In this book the author explains very beautiful links between pseudodifferential analysis and the theory of nonholomorphic modular forms on the classical modular group ... . The book is excellently written and represents an extremely valuable contribution for the two research communities - analysts from PDEs and pseudodifferential operators and number theorists. It exhibits a lot of new and original links between the two research areas. It is self-contained and easily accessible for a broad readership." (Soren Krausshar, Zentralblatt MATH, Vol. 1243, 2012)

• Introduction.- The Weyl calculus.- The Radon transformation and applications.- Automorphic functions and automorphic distributions.- A class of Poincaré series.- Spectral decomposition of the Poincaré summation process.- The totally radial Weyl calculus and arithmetic.- Should one generalize the Weyl calculus to an adelic setting?.- Index of notation.- Subject Index.- Bibliography.

From the reviews: "The book is devoted to explaining a close relationship between the pseudodifferential analysis and the well-known theory of automorphic functions and modular forms on the upper Poincare half-plane II, or their generalization as automorphic distributions. ... the book is perfectly readable and rich with analytic details for both researchers in pseudodifferential analysis and for number theorists." (Do Ngoc Diep, Mathematical Reviews, November, 2013) "In this book the author explains very beautiful links between pseudodifferential analysis and the theory of nonholomorphic modular forms on the classical modular group ... . The book is excellently written and represents an extremely valuable contribution for the two research communities - analysts from PDEs and pseudodifferential operators and number theorists. It exhibits a lot of new and original links between the two research areas. It is self-contained and easily accessible for a broad readership." (Soren Krausshar, Zentralblatt MATH, Vol. 1243, 2012)

• Introduction.- The Weyl calculus.- The Radon transformation and applications.- Automorphic functions and automorphic distributions.- A class of Poincaré series.- Spectral decomposition of the Poincaré summation process.- The totally radial Weyl calculus and arithmetic.- Should one generalize the Weyl calculus to an adelic setting?.- Index of notation.- Subject Index.- Bibliography.