Real Linear Operator Theory and its Applications

Real linear operators arise in a range of applications of mathematical physics. In this paper, basic properties of real linear operators are studied and their spectral theory is developed. Suitable extensions of classical operator theoretic concepts are introduced. Providing a concrete class, real linear multiplication operators are investigated and, motivated by the Beltrami equation, related problems of unitary approximation are addressed.

[1]  H. Shapiro,et al.  The Friedrichs operator of a planar domain. II , 2000 .

[2]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[3]  F. Smithies.  A HILBERT SPACE PROBLEM BOOK , 1968 .

[4]  Pierre Deligne,et al.  Quantum Fields and Strings: A Course for Mathematicians , 1999 .

[5]  M. Birkner,et al.  Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach , 2002 .

[6]  Bernard Aupetit,et al.  A Primer on Spectral Theory , 1990 .

[7]  K. Friedrichs.  On certain inequalities and characteristic value problems for analytic functions and for functions of two variables , 1937 .

[8]  Samuli Siltanen,et al.  Numerical solution method for the dbar-equation in the plane , 2004 .

[9]  Stephan Ramon Garcia,et al.  Complex Symmetric Operators and Applications II , 2005 .

[10]  Kari Astala,et al.  Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48) , 2009 .

[11]  E. Guth,et al.  Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren , 1932 .

[12]  O. Nevanlinna,et al.  Real linear matrix analysis , 2007 .

[13]  Samuli Siltanen,et al.  Numerical computation of complex geometrical optics solutions to the conductivity equation , 2010 .

[14]  Tadeusz Iwaniec,et al.  Geometric Function Theory and Non-linear Analysis , 2002 .

[15]  Kari Astala,et al.  Calderon's inverse conductivity problem in the plane , 2006 .

[16]  P. Halmos,et al.  Algebraic Properties of Toeplitz operators. , 1964 .

[17]  P. Halmos.  A Hilbert Space Problem Book , 1967 .

[18]  R. Rochberg,et al.  On the Friedrichs operator , 1995 .

[19]  Tadeusz Iwaniec,et al.  The Beltrami Equation , 2007 .

[20]  V. Bargmann.  NOTE ON WIGNER'S THEOREM ON SYMMETRY OPERATIONS , 1964 .