TY  - JOUR
A1  - Bär, Christian
A1  - Bandara, Lashi
T1  - Boundary value problems for general first-order elliptic differential operators
JF  - Journal of functional analysis
N2  - We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.
KW  - elliptic differential operators of firstorder
KW  - elliptic boundary
KW  - conditions
KW  - boundary regularity
KW  - Fredholm property
KW  - H-infinity-functional calculus
KW  - maximal regularity
KW  - Rarita-Schwinger
KW  - operator
Y1  - 2022
U6  - https://doi.org/10.1016/j.jfa.2022.109445
SN  - 0022-1236
SN  - 1096-0783
VL  - 282
IS  - 12
PB  - Elsevier
CY  - Amsterdam [u.a.]
ER  - 
TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Boundary problems on a manifold with edge
JF  - Asian-European Journal of Mathematics
N2  - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.
KW  - manifolds with edge and boundary
KW  - distribution with asymptotics
KW  - ellipticity
KW  - Fredholm property
Y1  - 2017
U6  - https://doi.org/10.1142/S1793557117500875
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Class of Toeplitz Operators in Several Variables
JF  - Advances in applied Clifford algebras
N2  - We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.
KW  - Cauchy data spaces
KW  - Laplace-Beltrami operator
KW  - Toeplitz operators
KW  - Fredholm property
Y1  - 2015
U6  - https://doi.org/10.1007/s00006-015-0546-9
SN  - 0188-7009
SN  - 1661-4909
VL  - 25
IS  - 4
SP  - 811
EP  - 828
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitri
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An index formula for Toeplitz operators
JF  - Complex variables and elliptic equations
N2  - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary.
KW  - Toeplitz operators
KW  - Fredholm property
KW  - index
KW  - Primary: 47B35
KW  - Secondary: 47L80
Y1  - 2015
U6  - https://doi.org/10.1080/17476933.2015.1050007
SN  - 1747-6933
SN  - 1747-6941
VL  - 60
IS  - 12
SP  - 1764
EP  - 1787
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  -