Inequalities for harmonic functions on spheroids and their applications

2001-06-01
Zahariuta, V
Hadamard-type interpolational inequalities for norms of harmonic functions are studied for confocal prolate and oblate spheroids. It is shown that the optimal level domains in such inequalities may be non-spheroidal. Moreover, in contrary with the case of analytic functions, there is an unremovable gap between the corresponding optimal level domains for inner and outer versions of Hadamard-type inequalities for harmonic functions. These results are based on some special asymptotical formulas for associated Legendre functions P-n(m), Q(n)(m), when the ratio m/n tends to some number gamma is an element of [0, 1]. The case of spheroids is studied in the frame of the general theory of so-called Lh-functions and extremal Lh-functions (Lh-potentials) (developed earlier by the author), which serves the harmonic functions case much as the theory of plurisubharmonic and maximal plurisubharmonic functions (pluripotentials) (Lelong, Bremermann, Siciak, Zahariuta, Bedford-Taylor, Sadullayev et al.) does in the case of analytic functions of several variables.
INDIANA UNIVERSITY MATHEMATICS JOURNAL

Suggestions

A note on the transfinite diameter of Bernstein sets
Yazıcı, Özcan (2022-01-01)
A compact set K subset of C-n is called Bernstein set if, for some constant M > 0, the following inequality
Value sets of bivariate Chebyshev maps over finite fields
Küçüksakallı, Ömer (2015-11-01)
We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.
Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Moller-Plesset perturbation theory
Bozkaya, Ugur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David (2011-09-14)
Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Moller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density ...
Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem
Dosi (Dosiev), A. A. (IOP Publishing, 2009-11-01)
We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra g. This is motivated by J. L. Taylor's programme of non-commutative holomorphic functional calculus in the Lie algebra framework.
Exact Solutions of Effective-Mass Dirac-Pauli Equation with an Electromagnetic Field
Arda, Altug; Sever, Ramazan (Springer Science and Business Media LLC, 2017-01-01)
The exact bound state solutions of the Dirac-Pauli equation are studied for an appropriate position-dependent mass function by using the Nikiforov-Uvarov method. For a central electric field having a shifted inverse linear term, all two kinds of solutions for bound states are obtained in closed forms.
Citation Formats
V. Zahariuta, “Inequalities for harmonic functions on spheroids and their applications,” INDIANA UNIVERSITY MATHEMATICS JOURNAL, pp. 1047–1075, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63753.