This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.
Overview.- Preface.- List of Figures.- Key Words.- Selected Key Results.- Glossary.- 1. Introduction.- 2 Distance and Tube Zeta Functions.- 3. Applications of Distance and Tube Zeta Functions.- 4. Relative Fractal Drums and Their Complex Dimensions.- 5.Fractal Tube Formulas and Complex Dimensions.- 6. Classification of Fractal Sets and Concluding Comments.- Appendix A. Tame Dirchlet-Type Integrals.- Appendix B. Local Distance Zeta Functions.- Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs.- Acknowledgements.- Bibliography.- Author Index.- Subject Index.
Gerald W Johnson, Michel L. Lapidus, Lance Nielsen, Lincoln) Johnson, Gerald W (Professor Emeritus, Professor Emeritus, University of Nebraska, Riverside) Lapidus, Michel L. (Professor of Mathematics, Professor of Mathematics, University of California, Creighton University) Nielsen, Lance (Professor of Mathematics, Professor of Mathematics, JOHNSON ET AL, Johnson Et Al
Gerald W Johnson, Michel L. Lapidus, Lance Nielsen, Lincoln) Johnson, Gerald W (Professor Emeritus, Professor Emeritus, University of Nebraska, Riverside) Lapidus, Michel L. (Professor of Mathematics, Professor of Mathematics, University of California, Creighton University) Nielsen, Lance (Professor of Mathematics, Professor of Mathematics, JOHNSON ET AL, Johnson Et Al