Schrödinger Equations and Diffusion Theory

Abstract

Many of the original research and survey monographs in pure and applied mathematics published by Birkhäuser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers.

Retinamorphic bichromatic Schrödinger metamedia

“…The automaton's cells are located inside a 2D array. They can perform basic operations with complex numbers (in different complex algebras 2 …”

“…Linear and nonlinear Schrodinger equations [2,3] are important members of the family of methods for image processing, computer vision, and computer graphics. Schrödinger transform of image as a new tool for image analysis was first given in [3].…”

Bernstein Processes Associated with a Markov Process

“…The equality (4.11) means that under P V B , the process (X t ) cannot reach the nodal set {(t, x) ∈ [0, 1] × E; φ(t, x)ψ(t, x) = 0}. It was at first established by Zheng [21] [10]) is both far from being complete and false: it is claimed that (4.11) follows from the fact that P V B (φ(t, X t )ψ(t, X t ) > 0) = 1 for each t fixed (trivial by (4.10)) and the right continuity of t → φ(t, X t ), which was not proved.…”

Retinamorphic color Schrödinger metamedia

“…Diffusion and Schrödinger equations (linear and nonlinear) [1,2] and real-valued Gauss, complex-valued Fresnel and Schrödinger transforms associated with them are important members of the family of methods for image processing, computer vision, and computer graphics. Schrödinger transform of image as a new tool for image analysis was first given in [2].…”