TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent edge calculus and corner parametrices
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.
KW  - Edge calculus
KW  - corner parametrices
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 12
SP  - 2021
EP  - 2051
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Mahmoudi, Mahdi Hedayat
A1  - Schulze, Bert-Wolfgang
T1  - Volterra operators in the edge-calculus
JF  - Analysis and Mathematical Physics
N2  - We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).
KW  - Volterra operator
KW  - Anisotropic pseudo-differential operators
KW  - Edge calculus
KW  - Operator-valued symbols of Mellin type
Y1  - 2018
U6  - https://doi.org/10.1007/s13324-018-0238-4
SN  - 1664-2368
SN  - 1664-235X
VL  - 8
IS  - 4
SP  - 551
EP  - 570
PB  - Springer
CY  - Basel
ER  -