Analysis

Andreas M. Hinz

University of Munich

Here is a list of my publications about topics in analysis.

Werner O. Amrein, Andreas M. Hinz, David B. Pearson (Eds.),
Sturm-Liouville Theory, Past and Present, Birkhäuser, Basel, 2005.

Topics from spectral theory of differential operators,
in: R. del Río, C. Villegas-Blas (Eds.), Spectral Theory of Schrödinger Operators,
American Mathematical Society, Providence RI, 2004, 1-50.

Self-adjointness of Schrödinger operators, in:
J. C. Misra (Ed.), Applicable Mathematics in the Golden Age, Narosa, New Delhi, 2003, 285-304.

The extraordinary spectral properties of radially periodic
Schrödinger operators, Proc. Indian Acad. Sci. Math. Sci. 112(2002), 85-98.

(with B. M. Brown, M. S. P. Eastham, and K. M. Schmid)
Distribution of eigenvalues in gaps of the essential spectrum
of Sturm-Liouville operators - a numerical approach,
J. Comput. Anal. Appl. 6(2004), 85-95.

Distribution of eigenvalues in the dense point spectrum of
Schrödinger operators, in: Weikard, R., Weinstein, G.,
Differential Equations and Mathematical Physics, American Mathematical
Society/International Press, Providence RI/Cambridge MA, 2000,
207-216.

(with J. Denzler ) Catenaria Vera - The True Catenary,
Exposition. Math. 17(1999), 117-142.

(with B. M. Brown , M. S. P. Eastham, T. Kriecherbauer ,
D. K. R. McCormack, and K. M. Schmidt)
Welsh Eigenvalues of Radially Periodic Schrödinger Operators,
J. Math. Anal. Appl. 225(1998), 347-357.

(with E. B. Davies ) Kato class potentials for higher order
elliptic operators , J. London Math. Soc. (2) 58(1998), 669-678.

(with E. B. Davies ) Explicit constants for Rellich inequalities
in L_p(Omega), Math. Z. 227(1998), 511-523.

Hölder Continuity of Weak Solutions of Schrödinger
Equations, in: Proceedings of the International Conference
on Differential Equations and Mathematical Physics, International
Press, Cambridge MA, 1995, 96-101.

Regularity of Solutions for Singular Schrödinger Equations,
in: W. F. Ames, E. M. Harrell II, J. V. Herold (Eds.),
Differential Equations with Applications to Mathematical Physics,
Academic Press, Boston, 1993, 167-176.

(with G. Stolz ) Polynomial boundedness of eigensolutions
and the spectrum of Schrödinger operators, Math.
Ann. 294(1992), 195-211.

Regularity of solutions for singular Schrödinger equations,
Rev. Math. Phys. 4(1992), 95-161.

(with R. Hempel , I. Herbst , and H. Kalf) Intervals of dense
point spectrum for spherically symmetric Schrödinger
operators of the type - Delta + cos(|x|), J. London Math.
Soc. (2) 43(1991), 295-304.

(with H. Kalf) Subsolution estimates and Harnack's inequality
for Schrödinger operators, J. Reine Angew. Math. 404(1990)
118-134.

Anyone interested in these topics may write to the e-mail address
below.

A joint project on "the distribution of eigenvalues in the dense
point spectrum of differential operators" with Cardiff University (Wales, U.K.)
(Prof. M. Brown and Dr. D. K. R. McCormack, and
Prof. M. Eastham) has been awarded an ARC grant by the DAAD and
British Council in 1996, extended until 1999.
My collaborators on this project at the LMU in Munich were
Prof. Dr. H. Kalf , Prof. T. Kriecherbauer PhD, and Priv.-Doz. K. M. Schmidt .
The results of that project are contained in the following publications:

A. M. Hinz, Distribution of eigenvalues in the dense point spectrum of
Schrödinger operators , in: Weikard, R., Weinstein, G.,
Differential Equations and Mathematical Physics, American Mathematical
Society/International Press, Providence RI/Cambridge MA, 2000,
207-216.

B. M. Brown, M. S. P. Eastham, A. M. Hinz, T. Kriecherbauer, D. K. R. McCormack,
and K. M. Schmidt, Welsh Eigenvalues of Radially Periodic Schrödinger Operators,
J. Math. Anal. Appl. 225(1998), 347-357.

B. M. Brown, M. S. P. Eastham, A. M. Hinz, and K. M. Schmidt,
Distribution of eigenvalues in gaps of the essential spectrum
of Sturm-Liouville operators - a numerical approach,
J. Comput. Anal. Appl. 6 (2004), 85-95.

K. M. Schmidt, Oscillation of the perturbed Hill equation and the lower
spectrum of radially periodic Schrödinger operators in the plane,
Proc. Amer. Math. Soc. 127 (1999), 2367-2374.

K. M. Schmidt, Critical coupling constants and eigenvalue asymptotics of
perturbed periodic Sturm-Liouville operators, Comm. Math. Phys. 211 (2000), 465-485.

K. M. Schmidt, Eigenvalues in gaps of perturbed periodic Dirac operators:
numerical evidence, J. Comput. Appl. Math. 148(2002), 169-181.

K. M. Schmidt, Eigenvalue asymptotics of perturbed periodic Dirac systems
in the slow-decay limit, Proc. Amer. Math. Soc. 131(2003), 1205-1214.

My further research interests cover the Tower of Hanoi and other topics .

Information on my courses and lectures is also available.

My coordinates are on my personal homepage .


A. M. Hinz, hinz@math.lmu.de, 2011-02-17