Self-Similar Energies on Finitely Ramified Fractals
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"Analysis of fractals began to take shape as a mathematical field in the late 1980s. Traditionally, the focus of analysis has been on finitely ramified fractals - those where copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive. On finitely ramified fractals, self-similar energies are derived from eigenforms - quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores conditions for the existence and uniqueness of these self-similar energ...
"Analysis of fractals began to take shape as a mathematical field in the late 1980s. Traditionally, the focus of analysis has been on finitely ramified fractals - those where copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive. On finitely ramified fractals, self-similar energies are derived from eigenforms - quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores conditions for the existence and uniqueness of these self-similar energies and addresses related problems. For certain cases, complete solutions are provided"-- Provided by publisher.
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