Generalized Fractal Strings Viewed as Measures

Michel L. Lapidus () and Machiel van Frankenhuysen ()
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Michel L. Lapidus: University of California, Department of Mathematics
Machiel van Frankenhuysen: University of California, Department of Mathematics

Chapter 3 in Fractal Geometry and Number Theory, 2000, pp 55-70 from Springer

Abstract: Abstract In Section 3.1 of this chapter, we introduce the notion of generalized fractal string, viewed as a measure on the half-line. We will use this notion in Chapter 4 to formulate our explicit formulas which will be applied throughout the remaining chapters. In Section 3.2, we discuss the spectrum of a generalized fractal string, and in Section 3.3, we briefly discuss the notion of generalized fractal spray, which will be used in Chapters 7 and 9.

Keywords: Zeta Function; Complex Dimension; Riemann Zeta Function; Meromorphic Continuation; Positive Borel Measure (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-5314-3_4

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