A01=Robert S. Strichartz
Analytic continuation
Analytic function
Asymptotic analysis
Author_Robert S. Strichartz
Boundary value problem
Calculation
Category=PBKJ
Category=PBMX
Change of variables
Coefficient
Continuous function
Continuous function (set theory)
Convergence of Fourier series
Decimation (signal processing)
Degeneracy (mathematics)
Difference quotient
Differentiable manifold
Differential calculus
Differential equation
Differential geometry
Differential operator
Dimension (vector space)
Directional derivative
Dirichlet boundary condition
Dirichlet eigenvalue
Dirichlet kernel
Distribution (mathematics)
Eigenfunction
Eigenvalues and eigenvectors
eq_isMigrated=0
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Euclidean space
Existential quantification
Explicit formulae (L-function)
Fractal analysis
Harmonic analysis
Harmonic function
Heat kernel
Hilbert space
Intersection (set theory)
Lebesgue constant (interpolation)
Linear algebra
Linear equation
Linear function
Lipschitz continuity
Mathematical induction
Mathematical optimization
Numerical integration
Ordinary differential equation
Orthonormal basis
Peano existence theorem
Periodic function
Polynomial
Power series
Proportionality (mathematics)
Pseudo-differential operator
Quadratic function
Removable singularity
Renormalization
Restriction (mathematics)
Riemann sum
Riemannian manifold
Self-similarity
Simultaneous equations
Spectral gap
Spectral theorem
Spline (mathematics)
Stone-Weierstrass theorem
System of linear equations
Tangent space
Theorem
Three-dimensional space (mathematics)
Trigonometric functions
Variable (mathematics)
Product details
- ISBN 9780691127316
- Weight: 255g
- Dimensions: 152 x 235mm
- Publication Date: 20 Aug 2006
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami.
Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course.
Robert S. Strichartz is Professor of Mathematics at Cornell University. He is the author of "The Way of Analysis" and "A Guide to Distribution Theory and Fourier Transforms".
