Spelling suggestions: "subject:"pseudopotential""
1 |
On a class of pseudo-differential operators in IRⁿMatjila, D M January 1988 (has links)
The class of pseudo-differential operators with symbols from Sm (superscript) po̧̧ (subscipt)(Ωx IRⁿ) has been extensively studied.The main assumption which characterises this class of symbols is that a(x,Ȩ) є Sm (superscript)po̧̧ (subscipt)(Ωx IRⁿ) should have a polynomial growth in the Ȩ variable only. The x-variable is controlled on compact subsets of Ω. A polynomial growth in both the x and Ȩ variables on a C°°(lR²ⁿ) function a(x,Ȩ) gives rise to a different class of symbols and a corresponding class of operators. In this work, such symbols and the action of the operators on the functional spaces S(lRⁿ) , S'(lRⁿ) and the Sobolev spaces Qs (superscript) (lRⁿ) (s є lRⁿ) are studied. A study of the calculus (i.e. transposes, adjoints and compositions) and the functional analysis of these operators is done with special attention to L-boundedness and compactness. The class of hypoelliptic pseudo-differential operators in IRⁿ is introduced as a subclass of those considered earlier.These operators possess the property that they allow a pseudo- inverse or parametrix. In conclusion. the spectral theory of these operators is considered. Since a general spectral theory would be beyond the scope of this work, only some special cases of the pseudo-differential operators in IRⁿ are considered. A few applications of this spectral theory are discussed
|
2 |
Global oscillatory integrals for solutions of hyperbolic systemsNicoll, Wilfred James January 1999 (has links)
No description available.
|
3 |
Pseudo-differential operators with rough coefficients /Wang, Luqi. January 1997 (has links)
Thesis ( Ph.D. ) -- McMaster University, 1997. / Includes bibliographical references (leaves 63-66). Also available via World Wide Web.
|
4 |
Euler solutions of pseudodifferential equationsSchulze, Bert-Wolfgang, Tarkhanov, Nikolai N. January 1998 (has links)
We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, 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 since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.
|
5 |
The edge algebra structure of boundary value problemsSchulze, Bert-Wolfgang, Seiler, Jörg January 2001 (has links)
Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.
|
6 |
Elliptische Topologie von TransmissionsproblemenBooss, Bernhelm, January 1972 (has links)
Thesis--Bonn. / Added t.p. with thesis statement. Summary in English. Includes bibliographical references (p. 47).
|
7 |
Box approximation and related techniques in spectral theoryBorovyk, Vita, January 2008 (has links)
Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 2, 2009) Vita. Includes bibliographical references.
|
8 |
Elliptische Topologie von TransmissionsproblemenBooss, Bernhelm, January 1972 (has links)
Thesis--Bonn. / Added t.p. with thesis statement. Summary in English. Includes bibliographical references (p. 47).
|
9 |
On a class of one-parameter operator semigroups with state space Rn x Zm generated by pseudo-differential operatorsMorris, Owen Christopher January 2013 (has links)
The thesis shows that, under suitable conditions, a pseudo-differential operator, defined on some "nice" set of functions on Rn x Zm, with continuous negative definite symbol q(x,xi,o) extends to a generator of a Feller semigroup. Sections 1-5 are the preliminary sections, these sections discuss some harmonic analysis concerning locally compact Abelian groups. The essence of this thesis are Sections 6-13, which deals with obtaining the estimates required for the fulfilment of the conditions of the Hille-Yosida-Ray theorem.
|
10 |
The Bourgain Spaces and Recovery of Magnetic and Electric Potentials of Schrödinger OperatorsZhang, Yaowei 01 January 2016 (has links)
We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in Cλ and the electric potential is of the form p1 + div p2 with p1, p2 ∈ Cλ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h2Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann map. Our results are in dimension three and higher.
|
Page generated in 1.3029 seconds