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Keywords
- elliptic operators (9)
- boundary value problems (8)
- index (8)
- K-theory (7)
- manifolds with singularities (6)
- pseudodifferential operators (6)
- relative index (6)
- Atiyah-Patodi-Singer theory (5)
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- elliptic operator (4)
- manifold with singularities (4)
- surgery (4)
- 'eta' invariant (3)
- Atiyah-Bott condition (3)
- boundary value problem (3)
- conical singularities (3)
- conormal symbol (3)
- differential operators (3)
- ellipticity (3)
- eta invariant (3)
- index of elliptic operators in subspaces (3)
- spectral flow (3)
- Atiyah-Bott obstruction (2)
- Carleman matrix (2)
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- Hodge theory (2)
- Laplace equation (2)
- Lefschetz fixed point formula (2)
- Mellin transform (2)
- Probabilistic Cellular Automata (2)
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- Zaremba problem (2)
- aerosol size distribution (2)
- cluster expansion (2)
- edge singularities (2)
- edge-degenerate operators (2)
- elliptic boundary value problems (2)
- elliptic complexes (2)
- elliptic families (2)
- elliptic family (2)
- elliptic system (2)
- eta-invariant (2)
- holomorphic solution (2)
- homotopy classification (2)
- ill-posed problem (2)
- index formulas (2)
- inversion (2)
- linking coefficients (2)
- manifolds with conical singularities (2)
- manifolds with edges (2)
- maximum likelihood estimator (2)
- modn-index (2)
- monodromy matrix (2)
- pseudo-differential boundary value problems (2)
- pseudodiferential operators (2)
- quantization (2)
- regularization (2)
- regularizer (2)
- regularizers (2)
- reversible measure (2)
- singular partial differential equation (2)
- star-product (2)
- symmetry conditions (2)
- the Cauchy problem (2)
- weighted edge spaces (2)
- weighted spaces (2)
- (co)boundary operator (1)
- APS problem (1)
- Approximate likelihood (1)
- Atiyah-Singer theorem (1)
- Attractive Dynamics (1)
- Beltrami equation (1)
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- C0−semigroup (1)
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- Elliptic operators in domains with edges (1)
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- Multidimensional nonisentropic hydrodynamic model (1)
- Multiwavelength LIDAR (1)
- Neumann problem (1)
- Non-linear (1)
- Nonlinear (1)
- Nonlinear Laplace operator (1)
- Operators on manifolds with conical singularities (1)
- Operators on manifolds with edge (1)
- Operators on manifolds with edge and conical exit to infinity (1)
- Perron's method (1)
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- Pseudodifferential operators (1)
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- Ramified Cauchy problem (1)
- Reciprocal process (1)
- Riemann-Roch theorem (1)
- SPECT (1)
- Saturation model (1)
- Second order elliptic equations (1)
- Sobolev problem (1)
- Sobolev spaces with double weights on singular cones (1)
- Stochastic Differential Equation (1)
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- Stochastic differential equations (1)
- Surface potentials with asymptotics (1)
- Survival models with covariates (1)
- System of nonlocal PDE of first order (1)
- Tikhonov regularization (1)
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- WKB method (1)
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- asymptotics of solutions (1)
- attenuated Radon transform (1)
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- bending of an orthotropic cusped plate (1)
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- censoring (1)
- classical and quantum reduction (1)
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- cohomology (1)
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- contact transformations (1)
- corner Sobolev spaces with double weights (1)
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- covering (1)
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- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- deformation quantization (1)
- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- detailed balance equation (1)
- dimension functional (1)
- discrete saymptotic types (1)
- division algebras (1)
- divisors (1)
- domains with singularities (1)
- duality formula (1)
- edge Sobolev spaces (1)
- edge algebra (1)
- edge spaces (1)
- edge symbol (1)
- elastic bar (1)
- elliptic functions (1)
- elliptic morphism (1)
- elliptic operators in subspaces (1)
- elliptic operators on non-compact manifolds (1)
- elliptic problem (1)
- elliptic systems (1)
- ellipticity in the edge calculus (1)
- ellipticity of cone operators (1)
- ellipticity of corners operators (1)
- ellipticity with interface conditions (1)
- ellipticity with respect to interior and edge symbols (1)
- energetic space (1)
- estimation of regression (1)
- exponential function (1)
- exponential stability (1)
- exterior tensor product (1)
- fibre coordinates (1)
- finiteness theorem (1)
- force unification (1)
- fully non-linear degenerate parabolic equations (1)
- fundamental solution (1)
- gauge group (1)
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- geometric optics approximation (1)
- global exact boundary controllability (1)
- global solution (1)
- global solutions (1)
- good-inner function (1)
- goodness of fit (1)
- hard core interaction (1)
- hard core potential (1)
- hyperbolic operators (1)
- illposed problem (1)
- index formula (1)
- index of elliptic operator (1)
- infinite-dimensional diffusion (1)
- integral formulas (1)
- interfaces with conical singularities (1)
- inverse ill-posed problem (1)
- kernel estimator of the hazard rate (1)
- least squares estimator (1)
- lifespan (1)
- limit theorem for integrated squared difference (1)
- local time (1)
- manifold with edge (1)
- manifolds with cusps (1)
- matching of asymptotic expansions (1)
- meromorphic family (1)
- metaplectic operators (1)
- mixed elliptic problems (1)
- mod k index (1)
- moduli space of flat connections (1)
- modulo n index (1)
- molecular motor (1)
- mollifier method (1)
- moment map (1)
- monotone coupling (1)
- monotone method (1)
- multilayered coated and absorbing aerosol (1)
- multiple characteristics (1)
- multiwavelength Lidar (1)
- multiwavelength lidar (1)
- new recursive algorithm (1)
- non-Markov drift (1)
- non-coercive boundary conditions (1)
- nondegenerate condition (1)
- nonhomogeneous boundary value problems (1)
- nonlinear invers problem (1)
- nonlinear optimization (1)
- nonlocal problem (1)
- norm estimates with respect to a parameter (1)
- normal reflection (1)
- operator algebras on manifolds with singularities (1)
- operators on manifolds with conical and edge singularities (1)
- operators on manifolds with edges (1)
- operators on manifolds with singularities (1)
- order reduction (1)
- parallelizable spheres (1)
- parameter-dependent cone operators (1)
- parameter-dependent ellipticity (1)
- parameter-dependent pseudodifferential operators (1)
- parity condition (1)
- parity conditions (1)
- polydisc (1)
- principal symbolic hierarchies (1)
- problem of classification (1)
- profile likelihood (1)
- propor-tional hazard mode (1)
- pseudo-diferential operators (1)
- pseudo-differential operators (1)
- pseudo-differentialboundary value problems (1)
- pseudodifferential boundary value problems (1)
- pseudodifferential operator (1)
- pseudodifferential subspace (1)
- pseudodifferential subspaces (1)
- reciprocal processes (1)
- relative cohomology (1)
- relative index formulas (1)
- relative η-invariant (1)
- residue (1)
- root functions (1)
- semiconductors (1)
- semiprocess (1)
- shock wave (1)
- small parameter (1)
- spectral boundary value problems (1)
- spectral independence (1)
- spectral resolution (1)
- spectral theorem (1)
- star product (1)
- stochastic ordering (1)
- subRiemannian geometry (1)
- symmetry group (1)
- symplectic (canonical) transformations (1)
- symplectic reduction (1)
- system Lame (1)
- systems of partial differential equations (1)
- time duality (1)
- time symmetry (1)
- tomogrphy (1)
- transition path theory (1)
- ultracontractivity (1)
- uniform compact attractor (1)
- variable projection method (1)
- vibration (1)
- weighted Sobolev space (1)
- weighted Sobolev spaces with discrete saymptotics (1)
- weighted spaces with asymptotics (1)
- η-invariant (1)
- ∂-operator (1)
Institute
- Institut für Mathematik (276) (remove)
It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.
The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.
The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too.
We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).
Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with Hölder continuous coeffcients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.
The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.
The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.