scholarly journals Scattering Theory for 4-th Order Differential Operators, I

1988 ◽  
Vol 14 (1) ◽  
pp. 1-57 ◽  
Author(s):  
Katsunori IWASAKI
Keyword(s):  
Scattering Theory ◽  
Differential Operators

scholarly journals Inverse nodal problem for nonlocal differential operators

2019 ◽  
Vol 50 (3) ◽  
pp. 337-347
Author(s):  
Xin-Jian Xu ◽  
Chuan-Fu Yang
Keyword(s):  
Boundary Condition ◽  
Scattering Theory ◽  
Differential Operators ◽  
Diffusion Processes ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Inverse Nodal Problem ◽  
Nodal Data ◽  
Nodal Problem ◽  
The Given

Inverse nodal problem consists in constructing operators from the given zeros of  their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.

CONVOLUTED GENERALIZED WHITE NOISE, SCHWINGER FUNCTIONS AND THEIR ANALYTIC CONTINUATION TO WIGHTMAN FUNCTIONS

1996 ◽  
Vol 08 (06) ◽  
pp. 763-817 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
HANNO GOTTSCHALK ◽  
JIANG-LUN WU
Keyword(s):  
White Noise ◽  
Analytic Continuation ◽  
Random Fields ◽  
Scattering Theory ◽  
Differential Operators ◽  
Cluster Property ◽  
Reflection Positivity ◽  
Equivalent Formulation ◽  
Pseudo Differential Operators ◽  
Moment Functions

We construct Euclidean random fields X over [Formula: see text] by convoluting generalized white noise F with some integral kernels G, as X=G*F. We study properties of Schwinger (or moment) functions of X. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Schwinger functions which we then apply to the above fields. We present a partial negative result on the reflection positivity of convoluted generalized white noise. Furthermore, by representing the kernels Gα of the pseudo-differential operators [Formula: see text] for α∈(0, 1) and m0>0 as Laplace transforms we perform the analytic continuation of the (truncated) Schwinger functions of X=Gα*F, obtaining the corresponding (truncated) Wightman distributions on Minkowski space which satisfy the relativistic postulates on invariance, spectral property, locality and cluster property. Finally we give some remarks on scattering theory for these models.

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