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  • 1
    Online Resource
    Online Resource
    Pseudo-differential operators on manifolds with singularities (1991)
    Amsterdam : North-Holland | New York, N.Y., U.S.A : Sole distributors for the United States and Canada, Elsevier Science Pub. Co
    Details Availability
    Keywords: Manifolds (Mathematics) ; Pseudodifferential operators ; Singularities (Mathematics) ; Differential equations ; Pseudodifferentialoperator ; Mannigfaltigkeit ; Singularität
    Type of Medium: Online Resource
    Pages: Online-Ressource , vi, 410 p , ill , 23 cm
    Edition: Online-Ausg.] Elsevier e-book collection on ScienceDirect
    ISBN: 0444881379 , 9780444881373
    Series Statement: Studies in mathematics and its applications v. 24
    URL: http://www.sciencedirect.com/science/book/9780444881373
    URL: https://zbmath.org/?q=an:0747.58003
    RVK:
    SK 620
    Language: English
    Note: Includes bibliographical references (p. [395]-401) and indexes
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  • 2
    Electronic Resource
    Electronic Resource
    A theory of pseudo-differential boundary value problems with discontinuous conditions I (1984)
    Springer
    Annals of global analysis and geometry 2 (1984), S. 163-251 
    Details
    ISSN: 1572-9060
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper deals with mixed boundary value problems and transmission problems for elliptic differential and pseudo-differential operators. These problems are considered as elements of an algebra (where Ω is the considered domain, x=∂Ω, Y⊂X a submanifold of codimension 1, where the conditions have a jump, and x∂ is a certain compactification of X/Y), the elements of which are described on a symbolic level. By means of additional conditions (of trace and potential type, with respect to Y) a given mixed problem is extended to an operator , and the Fredholm property of is established under an ellipticity condition, the parametrix is constructed on symbolic level and ind is expressed. In the second part the authors also study classes of special cases, namely differential operators of second and higher order with mixed boundary conditions for dim Ω≧2, where explicit index expressions are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876508
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  • 3
    Electronic Resource
    Electronic Resource
    A theory of pseudo-differential boundary value problems with discontinuous conditions II (1984)
    Springer
    Annals of global analysis and geometry 2 (1984), S. 289-384 
    Details
    ISSN: 1572-9060
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876418
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    The Atiyah–Bott–Lefschetz Theorem for Manifolds with Conical Singularities (1999)
    Springer
    Annals of global analysis and geometry 17 (1999), S. 409-439 
    Details
    ISSN: 1572-9060
    Keywords: conical singularities ; elliptic operator ; Fredholm property ; Lefschetz fixed point formula ; Lefschetz number ; pseudodifferential operators ; regularizer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish an Atiyah–Bott–Lefschetz formula for elliptic operators on manifolds with conical singular points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006509003512
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  • 5
    Electronic Resource
    Electronic Resource
    Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics (1986)
    Springer
    Annals of global analysis and geometry 4 (1986), S. 137-223 
    Details
    ISSN: 1572-9060
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00129908
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  • 6
    Electronic Resource
    Electronic Resource
    Pseudo-differential operators with operator-valued symbols in the Mellin-edge-approach (1994)
    Springer
    Annals of global analysis and geometry 12 (1994), S. 135-171 
    Details
    ISSN: 1572-9060
    Keywords: Pseudo-differential operators ; Mellin transform ; corner problems ; wedge Sobolev spaces ; 35 S 05 ; 46 E 40 ; 58 G 15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The pseudo-differential Mellin-edge-approach is a tool for studying differential and pseudo-differential operators on manifolds with corners. The Mellin transform, acting on the corner axis ℝ+, is a substitute for the Fourier transform along edge variables in the calculus of wedge pseudo-differential operators. The basic elements of that theory (cf. Schulze [6,8]) are extended to edges like ℝ+ ∋ t with a control of symbols and smoothing operators near the vertext=0. The authors study the weighted Mellin wedge Sobolev spaces, the operator-valued Mellin convention translating Fourier symbols into Mellin ones under preserved smoothness up tot=0, and develop an operator calculus with its characterization on the level of symbols. Throughout the theory, there are involved one-parameter groups of isomorphisms acting on the Banach spaces that are the abstract analogues of the weighted cone Sobolev spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02108294
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  • 7
    Electronic Resource
    Electronic Resource
    On the Index of Differential Operators on Manifolds with Conical Singularities (1998)
    Springer
    Annals of global analysis and geometry 16 (1998), S. 141-172 
    Details
    ISSN: 1572-9060
    Keywords: analytic index ; Atiyah–Singer theorem ; conical singularities ; ellipticity ; Eulercharacteristics ; Fredholm operators ; Mellintransform ; pseudodifferential operators ; regularizers ; trace class
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006521714633
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  • 8
    Electronic Resource
    Electronic Resource
    An Operator Algebra on Manifolds with Cusp-Type Singularities (1998)
    Springer
    Annals of global analysis and geometry 16 (1998), S. 101-140 
    Details
    ISSN: 1572-9060
    Keywords: asymptotic expansions ; Borel–Laplace transform ; cusps ; ellipticity ; elliptic theory ; endless continuability ; finiteness theorem ; Fredholm property ; left ordered representation ; local casp algebra ; manifolds with singularities ; noncommutative analysis ; regularizer ; resurgent analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Equations on manifolds with cusp-type singularities are investigated. The corresponding calculus of pseudodifferential operators is constructed and finiteness theorems (Fredholm property) are established. The resurgent character of solutions is proved for equations with infinitely flat right-hand side.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006565731471
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  • 9
    Electronic Resource
    Electronic Resource
    Euler solutions of pseudodifferential equations (1999)
    Springer
    Integral equations and operator theory 33 (1999), S. 98-123 
    Details
    ISSN: 1420-8989
    Keywords: primary: 45N05 ; secondary: 34G10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a homogeneous pseudodifferential equation on a cylinderC=ℜ×X over a smooth compact closed manifoldX whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators overX. When assuming the symbol to be independent on the variablet ∈ ℜ, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points sinceC can be thought of as a ‘stretched’ manifold with conical points att=−∞ andt=∞. When compared with the general theory, our approach is constructive while highlighting all the features of this latter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01203082
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