Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations

In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Z_p which are the inverse limit of the finite rings Z/pⁿ. This gives rise to a tree, and probability measures w on Z_p correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L₂(Z_p,w). The real analogue of the p-adic integers is the interval [-1,1], and a prob...