Mathematics

Technical Publications

Journal Articles

    1. Lapidus, M.L. 1980. "Formules de Moyenne et de Produit pour les Résolvantes Imaginaires d' Opérateurs Auto-Adjoints", [Mean and Product Formulas for Imaginary Resolvents of Self-Adjoint Operators] . Comptes Rendus de l'Academie des Sciences, Paris Ser. A 291; MR 8lj:47016; Zbl 446:47010. p.451-454. 4p. (Refereed)  

    2. Lapidus, M.L. 1980. "Généralisation de las Formule de Trotter-Lie", [Generalization of the Trotter-Lie Formula]. Comptes Rendus de l'Academie des Sciences, Paris Ser.; MR 8lk:47092; Zbl 447:47023. p.479-500. 12p. (Refereed)  

    3. Lapidus, M.L. 1980. "Perturbation d' un Semi-groupe par un Groupe Unitair", [Perturbation of a Semigroup by a Unitary Group]. Comptes Rendus de l'Academie des Sciences, Paris Ser. A 291, MR 82d:47046; Zbl 447:47022. p.535-538. 4p. (Refereed)  

    4. Lapidus, M.L. 1980. :Generalization of the Trotter-Lie Formula. Integral Equations and Operator Theory 4, MR 83e:47057; Zbl 463:47824. p.366-415. 50p. (Refereed)  

    5. Lapidus, M.L. 1982. "Modification de 'Intégrale de Feynman pour un Potentiel Positif Singulier:  Approche Séquentielle", [Modification of the Feynman Integral for a Nonnegative Singular Potential:  Sequential Approach]. Comptes Rendus de l'Academie des Sciences, Paris Ser., I Math 195 MR 83b:81028; Zbl 493:35038. p.1-3. 3p. (Refereed)  

    6. Lapidus, M.L. 1982. "Intégrale de Feynman Modifiée et Formule du Produit pour un Potentiel Singulier Négatif", [Modified Feynman Integral and Product Formula for a Negative Singular Potential]. Comptes rendus de l'Academie des Sciences Paris, Ser. I Math. 295; MR 85h:35065; Zbl 508.35027. p.719-722. 4p. (Refereed)  

    7. Lapidus, M.L. 1984. "Valeurs Propres du Laplacien avec un Poids qui Change de Signe, [Eigenvalues of the Laplacian with an Indefinite Weight Function]. Comptes Rendus de l'Academie des Sciences Paris Ser. I Math. 298; MR 85j:35139. p.265-268. 4p. (Refereed)  

    8. Lapidus, M.L. 1985. "Product Formula for Imaginary Resolvents wth Application to a Modified Feynman Integral. Journal of Functional Analysis 63; MR 87c:47059. p.261-275. 15p. (Refereed)  

    9. Lapidus, M.L. 1985. "Perturbation Theory and a Dominated Convergene Theorem for Feynman Integrals". Integral Equations and Operator Theory 8; MR 86g:81036. p.36-62. 27p. (Refereed)  

    10. Lapidus, M.L., Fleckinger, J. 1986. "Eigenvalues of Elliptic Boundary Value Problems with an Indefinite Weight Function". Transactions of the American Mathematical Society 295; MR 87j:35382. p.305-324. 20p. (Refereed)  

    11. Lapidus, M.L. 1986. "The Differential Equation for the Feynman-Kac Formula with a Lebesgue-Stieltjes Measure". Letters in Mathematical Physics 11; MR 87d:58033. p.1-31. 31p. (Refereed)  

    12. Lapidus, M.L., Johnson, G.W. 1986. "Generalized Dyson Series, Generalized Feynman Diagrams, the Feynman Integral and Feynman's Operational Calculus". Memoirs of the American Mathematical Society, No. 351, 62; MR 88f:81034. p.1-78. 78p. (Refereed)  

    13. Lapidus, M.L. 1987. "The Feynman-Kac Formula with a Lebesgue-Stieltjes Measure and Feynman's Operational Calculus". Studies in Applied Mathematics 76. p.93-132. 40p. (Refereed)  

    14. Lapidus, M.L. 1987. "Strong Product Integration of Measures and the Feynman-Kac Formula with a Lebesgue-Stieltjes Measure". Supplemento ai Rendiconti del Circolo Matematico di Palermo, Ser. II, 17. p.271-312. 42p. (Refereed)  

    15. Lapidus, M.L., Johnson, G.W. 1987. "Une Multiplication Non Commutative des Fonctionnelles de Wiener et le Calcul Opérationel de Feynman", [A Noncommutative Multiplication of Wiener Functionals and Feynman's Operational Calculus]. Comptes Rendus de l'Academie des Sciences Paris Ser. I Math 304. p.523-526. 4p. (Refereed)  

    16. Lapidus, M.L. 1987. Remainder Estimates for the Asymptotics of Elliptic
eigenvalue Problems with Indefinite Weights". Archives for Rational Mechanics and Analysis 98. p.329-356. 28p. (Refereed)  

    17. Lapidus, M.L., Fleckinger, J. 1988. "Tambour Fractal:  Vers une Resolution de la Conjecture de Weyl-Berry pour les Valeurs Propres du Laplacien:, [Fractal Drum:  Towards a Resolution of the Weyl-Berry Conjecture for the Eigenvalues of the Laplacian]. Comptes Rendus de l'Academie des Sciences Paris Ser. I Math. 306. p.171-175. 5p. (Refereed)  

    18. Lapidus, M.L., Johnson, G.W. 1988. "Noncommutative Operations on Wiener Functionals and Feynman's Operational Calculuc". Journal of Functional Analysis 81. p.74-99. 26p. (Refereed)  

    19. Lapidus, M.L. 1989. "The Feynman-Kac Formula with a Lebesgue-Stieltjes Measure: An Integral Equation in the General Case". Integral Equations and Operator Theory 12 (1989). p.163-210. 48p. (Refereed)  

    20. Lapidus, M.L. 1989. "Quantification, Calcul de feynman Axiomatique et Intégrale Fonctionnelle Généralisée", [Quantization, Axiomatic Feynman's Operational Calculus and Generalized Functional Integral]. Comptes Rendus de l'Academie des Sciences Paris Ser. I Math. 308. p.133-138. 6p. (Refereed)  

    21. Pomerance, C., Pomerance, C. 1990. "La Fonction Zêta de Riemann et la conjecture de Weyl-Berry pour les Tambours Fractals", [The Riemann Zeta-Function and the Weyl-Berry Conjecture for Fractal Drums]. Comptes Rendus de l'Academie des Sciences Paris Ser. I Math. 310. p.343-348. 6p. (Refereed)  

    22. Lapidus, M.L., Weinholtz, A.B. 1990. "Product Formula for Normal Operators and the Modified Feynman Integral". Proceedings of the American Mathematical Society 110. p.449-460. 12p. (Refereed)  

    23. Lapidus, M.L., Maier, H. 1991. "Hypothése de Riemann, Cordes Fractales Vibrantes et Conjecture de Weyl-Berry Modifiée", [The Riemann Hypothesis, Vibrating Fractal Strings and the Modified Weyl-Berry conjecture]. Comptes Rendus de l'Academie des Sciences Paris Ser. I Math. 313. p.19-24. 6p. (Refereed)  

    24. Lapidus, M.L. 1991. "Fractal Drum, Inverse Spectral Problems for Elliptic Oerators and a Partial Resolution of the Weyl-Berry Conjecture". Transactions of the American Mathematical Society 325. p.465-529. 65p. (Refereed)  

    25. Lapidus, M.L., Kigami, J. 1993. "Weyl's Problem for the spectral diatribution of Laplacians on P.C.F.  Self-Similar Fractals". Communications in Mathematical Physics 158. p.93-125. 33p. (Refereed)  

    26. Lapidus, M.L., Pomerance, C. 1993. "The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums". Proceedings of the London Mathematical Society (3) 66. p.41-69. 29p. (Refereed)  

    27. Lapidus, M.L., Fleckinger, J. 1994. "Schrödinger Operators with Indefinite Weights:  Asymptotics of Eigenvalues with Remainder Estimates". Differential and Integral Equations u. p.1389-1418. 30p. (Refereed) 

    28. Lapidus, M.L. 1994. "Analysis on Fractals, Laplacians on Self-Similar Sets, Noncommutative Geometry and Spectral Demensions. Topological Methods in Nonlinear Analysis 4, No. 1. p.137-195. 59p. (Refereed)  

    29. Lapidus, M.L., Fleckinger, J. 1995. "Indefinite Elliptic Boundary Value Proble,s on Irregular Domains". Prodeedings of the American Mathematical Society 125. p.513-526. 14p. (Refereed) 

    30. Lapidus, M.L., Maier, H. 1995. "The Riemann Hypothesis and Inverse Spectral Problem for Fractal Drums". Proceedings of the London Mathematical Society. p.15-35. 21p. (Refereed)  

    31. Lapidus, M.L., Pang, M. 1995. "Eigenfunctions of the Koch Snowflake Drum". Communications in Mathematical Physics 172. p.359-376. 18p. (Refereed)  

    32. Lapidus, M.L. 1995. "Fractals and Vibrations:  Can You Hear the Shape of a Fractal Drum?". Fractals 3, No. 3. p.725-736. 12p. (Refereed)  

    33. Lapidus, M.L., Pomerance, C. 1996. Counterexamples to the Modified Weyl-Berry Conjecture". Mathematical Proceedings of the Cambridge Philosophical Society, 119. p.167-178. 12p. (Refereed)  

    34. Lapidus, M.L., He, C.Q. 1996. "Generalized Minkowski Content and the Vibrations of Fractal Drums and Strings". Mathematical Research Letters I. p.31-40. 10p. (Refereed)  

    35. Lapidus, M.L. 1996. "Feyman's Operational Calculus:  A Heuristic and Mathematical Introduction" (Special issue dedicated to the memory of Prof. Albert Badrikian). Annales Mathematiques Blaise Pascal 3. p.89-102. 14p. (Refereed)  

    36. Lapidus, M.L., Neuberger, J.W., Renka, R.J., Griffin, C.A. 1996. "Snowflake Harmonics and Computer Graphics: Nurmerical Computation of Spectra on Fractal Domains"; (Includes 23 computer graphics color plates). International Journal of Bifurcation and Chaos 6. p.1185-1210. 26p. (Refereed)  

    37. Lapidus, M.L., DeFacio, B., Johnson, G.W. 1997. "Feynman's Operational Calculus and Evolution Equations". Acta Mathematicae Applicandae 47. p.155-211. 57p. (Refereed)  

    38. Lapidus, M.L., He, C.Q. 1997. "Generalized Minkowski Content, Spectrum of Drums, Fractal Strings and the Riemann Zeta-Function". Memoirs of the Americal Mathematical Society No. 608, 127. p.1-97. 97p. (Refereed)  

    39. Lapidus, M.L., Kigami, J. 2001. "Self-Similarity of Volume Measures for Laplacians on P.C.F. Self-Fractals". Communications in Mathematical Physics 217. p.165-180. 16p. (Refereed)  

    40. Lapidus, M.L., van Frankenhuysen, M. 2003. "Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation". Journal of Experimental Mathematics, No. 1. p.41-69. 29p. (Refereed)  

Books

    1. Lapidus, M.L., Andersson, S.I. 1997. Progress in Inverse Spectral Geometry. Birkhauser. 196p. (Refereed)  

    2. Lapidus, M.L., Harper, L.H., Rumbos, A.J. 1997. Harmonic Analysis and Nonlinear Differential Equations. American Mathmatical Society. 350p. (Refereed) 

    3. Lapidus, M.L., Johnson, G.W. 2000. The Feynman Integral and Feynman's Operational Calculus. Clarendon Press. 771p. (Refereed) 

    4. Lapidus, M.L., van Frankenhuysen, M. 2000. Fractal Geometry and Number Theory. Birkhauser. 266p. (Refereed)  

Conference and Symposia Proceedings

    1. Lapidus, M.L. 1984. "Spectral Theory of Elliptic Problems with Indefinite Weights". Spectal Theory. p.159-168. 10p. Argonne National Laboratory, Argonne. (Refereed, )  

    2. Lapidus, M.L. 1984. "Product Formula for Imaginary Resolvents, Modified Feynman Integral and a General Dominated Convergence Theorem". Semesterbereich Funcktionalanalysis Sommersemester 84. p.9-24. 16p. Mathematisches Institut Eberhard-Karls-Universitat Tubingen. (Refereed, )  

    3. Lapidus, M.L. 1986. "Asymptotic Distribution of the Eigenvalues of Elliptic Boundary Value Problems and Schrödinger Operators with Indefinite Wwights". in Partial Differential Equations. p.9-24. 16p. Proc. VIIIth Latin American School of Mathematics, IMPA, Rio de Janeiro, Brazil. (Refereed, , Invited)  

    4. Lapidus, M.L. 1986. "Product Formula Imaginary Resolvents and Modified Feynman Integral". Proc. of Symposia in Pure Mathematics, American Mathematical Society 45; MR 87j:47059. p.109-112. 4p. (Refereed, )  

    5. Lapidus, M.L., Johnson, G.W. 1987. "Feyman's Operational Calculus, Generalized dyson Series and the Feynman Integral". Contemporary Mathematics, American Mathematical Society 62; MR 88c:81025. p.437-445. (Refereed, , Invited)  

    6. Lapidus, M.L. 1987. "The feynman Integral, the Feynman-Kac Formula with a Lebesgue-Stieltjes Measure and Feynman's Operational Calculus". Path Summation: Achievement and Goals. p.327-335. 9p. World Scientific, Singapore. (Refereed, , Invited)