scholarly journals A local form for the automorphisms of the spectral unit ball

2008 ◽  
Vol 59 (3) ◽  
pp. 321-324 ◽  
Author(s):  
Pascal J. Thomas
Keyword(s):  
Unit Ball ◽  
Local Form ◽  
Spectral Unit Ball

Holomorphic Self-Maps of the Spectral unit Ball

1991 ◽  
Vol 23 (3) ◽  
pp. 256-262 ◽  
Author(s):  
T. J. Ransford ◽  
M. C. White
Keyword(s):  
Unit Ball ◽  
Spectral Unit Ball

scholarly journals On the zero set of the Kobayashi–Royden pseudometric of the spectral unit ball

2008 ◽  
Vol 93 (1) ◽  
pp. 53-68
Author(s):  
Nikolai Nikolov ◽  
Pascal J. Thomas
Keyword(s):  
Unit Ball ◽  
Zero Set ◽  
Spectral Unit Ball

scholarly journals On the automorphisms of the spectral unit ball

2003 ◽  
Vol 155 (3) ◽  
pp. 207-230 ◽  
Author(s):  
Jérémie Rostand
Keyword(s):  
Unit Ball ◽  
Spectral Unit Ball

scholarly journals Certain non-homogeneous matricial domains and Pick–Nevanlinna interpolation problem

2021 ◽  
pp. 2150083
Author(s):  
Vikramjeet Singh Chandel
Keyword(s):  
Automorphism Group ◽  
Unit Ball ◽  
Complex Plane ◽  
Unit Disc ◽  
Interpolation Problem ◽  
Necessary Conditions ◽  
Holomorphic Automorphism ◽  
Spectral Unit Ball ◽  
Holomorphic Automorphism Group

In this paper, we consider certain matricial domains that are naturally associated to a given domain of the complex plane. A particular example of such domains is the spectral unit ball. We present several results for these matricial domains. Our first result shows — generalizing a result of Ransford–White for the spectral unit ball — that the holomorphic automorphism group of these matricial domains does not act transitively. We also consider [Formula: see text]-point and [Formula: see text]-point Pick–Nevanlinna interpolation problem from the unit disc to these matricial domains. We present results providing necessary conditions for the existence of a holomorphic interpolant for these problems. In particular, we shall observe that these results are generalizations of the results provided by Bharali and Chandel related to these problems.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

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