scholarly journals Functional model for extensions of symmetric operators and applications to scattering theory

2018 ◽  
Vol 13 (2) ◽  
pp. 191-215 ◽  
Author(s):  
Kirill D. Cherednichenko ◽  
◽  
Alexander V. Kiselev ◽  
Luis O. Silva ◽  
◽  
...  
Keyword(s):  
Scattering Theory ◽  
Functional Model ◽  
Symmetric Operators

Smooth derivations commuting with Lie group actions

1986 ◽  
Vol 99 (2) ◽  
pp. 307-314
Author(s):  
F. M. Goodman ◽  
P. E. T. Jorgensen ◽  
C. Peligrad
Keyword(s):  
Hilbert Space ◽  
Unitary Representation ◽  
Lie Group ◽  
Scattering Theory ◽  
Relativistic Quantum ◽  
Quantum Scattering ◽  
Quantum Scattering Theory ◽  
Lie Group Actions ◽  
Physical Setting ◽  
Symmetric Operators

N. S. Poulsen, motivated in part by questions from relativistic quantum scattering theory, studied symmetric operators S in Hilbert space commuting with a unitary representation U of a Lie group G. (The group of interest in the physical setting is the Poincaré group.) He proved ([17], corollary 2·2) that if S is defined on the space of C∞-vectors for U (i.e. D(S) ⊇ ℋ∞(U)), then S is essentially self-adjoint.

Spectral analysis of dissipative Schrödinger operators

1997 ◽  
Vol 127 (6) ◽  
pp. 1113-1121 ◽  
Author(s):  
B. P. Allahverdiev ◽  
Ahmet Canoǧlu
Keyword(s):  
Characteristic Function ◽  
Schrödinger Operators ◽  
Functional Model ◽  
Dissipative Operator ◽  
Schrodinger Operators ◽  
Associated Functions ◽  
Index 2 ◽  
Eigenfunctions And Associated Functions ◽  
Spectral Representations ◽  
Symmetric Operators

Dissipative Schrodinger operators are studied in L2(0, ∞) which are extensions of symmetric operators with defect index (2, 2). We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix according to the scheme of Lax and Phillips. With the help of the incoming spectral representation, we construct a functional model of the dissipative operator and construct its characteristic function in terms of solutions of the corresponding differential equation. On the basis of the results obtained regarding the theory of the characteristic function, we prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operator.

scholarly journals Dissipative Dirac operator with general boundary conditions on time scales

2020 ◽  
Vol 72 (5) ◽  
Author(s):  
B. P. Allahverdiev ◽  
H. Tuna
Keyword(s):  
Dirac Operator ◽  
Boundary Conditions ◽  
Time Scales ◽  
Functional Model ◽  
Scattering Matrix ◽  
The Other ◽  
General Boundary ◽  
Dissipative Operator ◽  
General Boundary Conditions ◽  
Symmetric Operators

UDC 517.9 In this paper, we consider the symmetric Dirac operator on bounded time scales. With general boundary conditions, we describe extensions (dissipative, accumulative, self-adjoint and the other) of such symmetric operators. We construct a self-adjoint dilation of dissipative operator. Hence, we determine the scattering matrix of dilation. Later, we construct a functional model of this operator and define its characteristic function. Finally, we prove that all root vectors of this operator are complete.

Southern Hemisphere Seti Survey: Five Years of Project Meta II

1997 ◽  
Vol 161 ◽  
pp. 611-621
Author(s):  
Guillermo A. Lemarchand ◽  
Fernando R. Colomb ◽  
E. Eduardo Hurrell ◽  
Juan Carlos Olalde
Keyword(s):  
Southern Hemisphere ◽  
Scattering Theory ◽  
Galactic Plane ◽  
Narrow Band ◽  
Neutral Hydrogen ◽  
Sky Survey ◽  
Inertial Frames ◽  
Interstellar Scattering ◽  
Extraterrestrial Origin ◽  
Spectral Channels

AbstractProject META II, a full sky survey for artificial narrow-band signals, has been conducted from one of the two 30-m radiotelescopes of the Instituto Argentino de Radioastronomía (IAR). The search was performed near the 1420 Mhz line of neutral hydrogen, using a 8.4 million channels Fourier spectrometer of 0.05 Hz resolution and 400 kHz instantaneous bandwidth. The observing frequency was corrected both for motions with respect to three astronomical inertial frames, and for the effect of Earths rotation, which provides a characteristic changing signature for narrow-band signals of extraterrestrial origin. Among the 2 × 1013spectral channels analyzed, 29 extra-statistical narrow-band events were found, exceeding the average threshold of 1.7 × 10−23Wm−2. The strongest signals that survive culling for terrestrial interference lie in or near the galactic plane. A description of the project META II observing scheme and results is made as well as the possible interpretation of the results using the Cordes-Lazio-Sagan model based in interstellar scattering theory.

Dynamical Scattering in Electron Diffraction of wet Protein Crystals

1980 ◽  
Vol 38 ◽  
pp. 42-43
Author(s):  
B. B. Chang ◽  
D. F. Parsons
Keyword(s):  
Electron Diffraction ◽  
Scattering Theory ◽  
Protein Crystals ◽  
Electron Diffraction Data ◽  
Specimen Thickness ◽  
Major Question ◽  
X Ray ◽  
Scattering Effects ◽  
Diffraction Patterns ◽  
Acceleration Voltage

The significance of dynamical scattering effects remains the major question in the structural analysis by electron diffraction of protein crystals preserved in the hydrated state. In the few cases (single layers of purple membrane and 400-600 Å thick catalase crystals examined at 100 kV acceleration voltage) where electron-diffraction patterns were used quantitatively, dynamical scattering effects were considered unimportant on the basis of a comparison with x-ray intensities. The kinematical treatment is usually justified by the thinness of the crystal. A theoretical investigation by Ho et al. using Cowley-Moodie multislice formulation of dynamical scattering theory and cytochrome b5as the test object2 suggests that kinematical analysis of electron diffraction data with 100-keV electrons would not likely be valid for specimen thickness of 300 Å or more. We have chosen to work with electron diffraction patterns obtained from actual wet protein crystals (rat hemoglobin crystals of thickness range 1000 to 2500 Å) at 200 and 1000 kV and to analyze these for dynamical effects.

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