TY  - JOUR
A1  - Chang, D. -C.
A1  - Viahmoudi, M. Hedayat
A1  - Schulze, Bert-Wolfgang
T1  - PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.
KW  - Pseudo-differential operators
KW  - boundary value problems
KW  - operator valued symbols
KW  - Fourier transform
Y1  - 2016
SN  - 1345-4773
SN  - 1880-5221
VL  - 17
SP  - 1889
EP  - 1937
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Schulze, Bert-Wolfgang
A1  - Wong, M. W.
T1  - Iterative properties of pseudo-differential operators on edge spaces
JF  - Journal of pseudo-differential operators and applications
N2  - Pseudo-differential operators with twisted symbolic estimates play a large role in the calculus on manifolds with edge singularities. We study here aspects of the underlying abstract concept and establish a new result on iteration of quantizations.
KW  - Pseudo-differential operators
KW  - Twisted symbolic estimates
KW  - Quantizations
Y1  - 2014
U6  - https://doi.org/10.1007/s11868-014-0100-x
SN  - 1662-9981
SN  - 1662-999X
VL  - 5
IS  - 4
SP  - 455
EP  - 479
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Chang, D. -C.
A1  - Schulze, Bert-Wolfgang
T1  - Calculus on spaces with higher singularities
JF  - Journal of pseudo-differential operators and applications
N2  - We establish extensions of the standard pseudo-differential calculus to specific classes of operators with operator-valued symbols occurring in symbolic hierarchies motivated by manifolds with higher singularities or stratified spaces.
KW  - Pseudo-differential operators
KW  - Operator-valued symbols
KW  - Fourier and Mellin transform
Y1  - 2017
U6  - https://doi.org/10.1007/s11868-016-0180-x
SN  - 1662-9981
SN  - 1662-999X
VL  - 8
SP  - 585
EP  - 622
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Analysis on regular corner spaces
JF  - The journal of geometric analysis
N2  - We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
KW  - Boutet de Monvel's calculus
KW  - Pseudo-differential operators
KW  - Singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - Parametrices of elliptic operators
KW  - Kegel space
Y1  - 2021
U6  - https://doi.org/10.1007/s12220-021-00614-3
SN  - 1050-6926
SN  - 1559-002X
VL  - 31
IS  - 9
SP  - 9199
EP  - 9240
PB  - Springer
CY  - New York
ER  -