Prof. Dr. Domenico P.L. Castrigiano

Technische Universität München Zentrum Mathematik - M7 Boltzmannstraße 3 85747 Garching Room: 03.08.058 Tel.: +49-89-289-17900 eMail: castrigma.tum.de Sprechzeiten nach Vereinbarung

Skripten

• Lineare Algebra für Physiker MA9201
• Analysis 1 für Physiker MA9202
• Analysis 2 für Physiker MA9203
• Analysis 3 für Physiker MA9204
• Spektraltheorie Linearer Operatoren MA5036

Research Interests

• Foundations of Quantum Mechanics
• Operator Theory
• Orthogonal Polynomials
• Singularity Theory, Catastrophe Theory
• Topological measures

Articles

• Castrigiano, D.P.L.; Mutze, U.: On the irreducible representations of groups containing a subgroup of finite index. - In: J. Math. Phys. 21 (1980), p. 956 - 960
• Castrigiano, D.P.L.; Henrichs, R. W.: Systems of covariance and subrepresentations of induced representations. - In: Lett. Math. Phys. 4 (1980), p. 169 -175
• Castrigiano, D.P.L.: Geometrical structures and the grinding process for three plates. - In: Structures and approximation in physical theories, ed. by A. Hartkämper and H. J. Schmidt, Plenum 1981, p. 237 - 247
• Castrigiano, D.P.L.: On Euclidean systems of covariance for massless particles. - In: Lett. Math. Phys. 5 (1981), p. 303 -309
• Castrigiano, D.P.L.; Süssmann, G.: Inertial Structure. I. - In: General Relativity and Gravitation 16 (1984), p. 867 - 875
• Castrigiano, D.P.L.; Süssmann, G.: Galilean Inertial Structure. II. - In: General Relativity and Gravitation 16 (1984), p. 893 - 900
• Castrigiano, D.P.L.: Metrical Geometry of Galilean Inertial Structure. III. - In: General Relativity and Gravitation 16 (1984), p. 901 - 908
• Castrigiano, D.P.L.; Kokiantonis, N.: Classical paths for a quadratic action with memory and exact evaluation of the path integral. - In: Physics Letters 96 A (1983), p. 55 - 60
• Castrigiano, D.P.L.: Causal transformations of Wightman localizations. - In: J. Math. Phys. 25 (1984), p. 1116 - 1121
• Castrigiano, D.P.L.; Kokiantonis, N.; Stierstorfer, H.: Free energy and effective mass of the polaron at finite temperatures. - In: Physics Letters 104 A (1984), p. 364 - 369
• Castrigiano, D.P.L.; Mutze, U.: Repeated measurements in quantum theory. - In: Physical Review A 30 (1984), p. 2210 - 2220
• Castrigiano, D.P.L.; Orthogonal polynomials and rigged Hilbert space. - In: J. Functional Analysis 65 (1986), p. 309 - 313
• Castrigiano, D.P.L.; Kokiantonis, N.: Quantum oscillator in a non-self-interacting radiation field: Exact calculation of the partition function. - In: Physical Review A 35 (1987), p. 4122 - 4128
• Castrigiano, D.P.L.; Kokiantonis, N.: Radiation damping of a quantum harmonic oscillator. - In: J. Phys. A: Math. Gen. 20 (1987), p. 4237 - 4245
• Castrigiano, D.P.L.; Stärk, F.: New aspects of the path integrational treatment of the Coulomb potential. - In: J. Math. Phys. 30 (1989), p. 2785 -2788
• Castrigiano, D.P.L.; Kokiantonis, N.; Stierstorfer, H.: Natural Spectrum of a Charged Quantum Oscillator. - In: Nuovo Cimento 108 B (1993), p. 765 - 777
• Castrigiano, D.P.L.; Klopfer, W.: Orthonormal bases of polynomials in one complex variable. - In: Analysis Mathematica 29 (2003), p. 7 - 14
• Betz, V.; Castrigiano, D.P.L.: Effective Density of States for a Quantum Oscillator Coupled to a Photon Field. - In: Commun. Math. Phys. 301, 811-839(2011) DOI 10.1007/s 00220-010-1167-8 (2010)
• Castrigiano, D.P.L.; Hofmaier, F.: Bounded point evaluations for orthogonal polynomials. - In: Advances and Applications in Mathematical Sciences 10(4) (2011), p. 373-392
• Zaigler, S.; Castrigiano, D.P.L.: Cyclicity for Unbounded Multiplication Operators in Lp- and Co-Spaces. In: Ann. Funct. Anal. 6(2), 33-48(2015) DOI 10.1532/afa/06-2-4
• Castrigiano, D.P.L.: Leiseifer, A.D.: Causal Localizations in Relativistic Quantum Mechanics. - In: J. Math. Phys. 56, 07230(2015) DOI 10.1063/1.4923196
• Castrigiano, D.P.L.: Dirac and Weyl Fermions - the only Causal Systems. - In: arxiv:1711.06556 (2017)
• Castrigiano, D.P.L.: Unbounded Wiener-Hopf Operators and Isomorphic Singular Integral Oprtators. - In: arxiv:2002.08116 (2020)
• Castrigiano, D.P.L.: Spectral Representations of the Wiener-Hopf Operator for the sinc Kernel and some Related Operators. - In: arXiv:2002.09235 (2020), Complex Anal. Oper.Theory 15(2021), https://doi.org/10.1007/s11785-021-01110-w
• Castrigiano, D.P.L.: Unbounded Toeplitz Operators with Rational Symbols. - In: arxiv:2010.06268 (2020), Mathematics and Statistics 9(5), p. 853-858 (2021), DOI: 10.13189/ms.2021.090525

Textbooks

Castrigiano, D.P.L., Hayes, S. A.: Catastrophe Theory. - 2nd Ed. Westview Press (Perseus Books Group) Advanced Book Program, Boulder 2004 264 pp. including 40 computer-generated graphics by Frank Hofmaier, 93 solved exercises, foreword by Rene Thom.

Castrigiano, D.P.L., Roelcke, W.: Topological Measures and Weighted Radon Measures, Alpha Science International Ltd., Oxford 2008 Due to the close interplay of measure and topology, topological measure theory is a particularly intriguing part of general measure theory. Appropriately this text starts with an introductory chapter on abstract measure theory. It presupposes some familiarity with elementary measure and integration theory and furnishes the prerequisites for the subsequent detailed exposition of the theory. The results mainly concern regularity properties of topological measures. The notions of mc measures and Lc spaces turn out to be particularly useful for the study of regularity properties of weighted Radon measures, a topic that was not treated previously in the literature. Because of the specific importance a whole chapter of purely topological content is devoted to Lc spaces. Throughout the textbook, the results are accompanied and consistently discussed by examples, ranging from routine to rather involved.

Current Research Projects

• Orthogonal polynomials and subnormal operators in collaboration with F. Hofmaier (TU München)
• Causal behavior of quantum systems in collaboration with A.D. Leiseifer (TU München)