The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Hao Cheng - One of the best experts on this subject based on the ideXlab platform.
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wavelets and numerical Pseudodifferential Operator
Applied Mathematical Modelling, 2016Co-Authors: Hao ChengAbstract:Abstract Calculating the value for the Pseudodifferential Operator with unbounded symbol is an ill-posed problem. In the present paper we adopt a wavelet regularization method to solve this problem, error estimates of Holder type between the regularized values and the exact values are derived. Applications of the general theory scheme and numerical test to the concrete problems are presented.
Charles H Conley - One of the best experts on this subject based on the ideXlab platform.
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equivalence classes of subquotients of supersymmetric Pseudodifferential Operator modules
Algebras and Representation Theory, 2015Co-Authors: Charles H ConleyAbstract:We study the equivalence classes of the non-resonant subquotients of spaces of Pseudodifferential Operators between tensor density modules over the superline \(\mathbb {R}^{1|1}\), as modules of the Lie superalgebra of contact vector fields. There is a 2-parameter family of subquotients with any given Jordan-Holder composition series. We give a complete set of even equivalence invariants for subquotients of all lengths l. In the critical case l = 6, the even equivalence classes within each non-resonant 2-parameter family are specified by a pencil of conics. In lengths l ≥ 7 our invariants are not fully simplified: for l = 7 we expect that there are only finitely many equivalences other than conjugation, and for l ≥ 8 we expect that conjugation is the only equivalence. We prove this in lengths l ≥ 15. We also analyze certain lacunary subquotients.
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equivalence classes of subquotients of supersymmetric Pseudodifferential Operator modules
arXiv: Representation Theory, 2013Co-Authors: Charles H ConleyAbstract:We study the equivalence classes of the non-resonant subquotients of spaces of Pseudodifferential Operators between tensor density modules over the 1|1 superline, as modules of the Lie superalgebra of contact vector fields. There is a 2-parameter family of subquotients with any given Jordan-Holder composition series. We give a complete set of even equivalence invariants for subquotients of all lengths. In the critical case of length 6, the even equivalence classes within each non-resonant 2-parameter family are specified by a pencil of conics. In lengths exceeding 6 our invariants are not fully simplified: in length 7 we expect that there are only finitely many equivalences other than conjugation, and in lengths exceeding 7 we expect that conjugation is the only equivalence. We prove this in lengths exceeding 14. We also analyze certain lacunary subquotients.
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equivalence classes of subquotients of Pseudodifferential Operator modules
arXiv: Representation Theory, 2013Co-Authors: Charles H Conley, Jeannette M LarsenAbstract:Consider the spaces of Pseudodifferential Operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There is a 2-parameter family of subquotients with any given Jordan-Holder composition series. In the critical case of subquotients of length 5, the equivalence classes within each non-resonant 2-parameter family are specified by the intersections of a pencil of conics with a pencil of cubics. In the case of resonant subquotients of length 4 with self-dual composition series, as well as of lacunary subquotients of lengths 3 and 4, equivalence is specified by a single pencil of conics. Non-resonant subquotients of length exceeding 7 admit no non-obvious equivalences. The cases of lengths 6 and 7 are unresolved.
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bounded subquotients of Pseudodifferential Operator modules
Communications in Mathematical Physics, 2005Co-Authors: Charles H ConleyAbstract:Recently there have been several papers on the action of the Virasoro Lie algebra on the projective decompositions of the modules of Pseudodifferential Operators on the circle. We use their results to prove that a wide class of the uniserial (completely indecomposable) bounded modules of the Virasoro Lie algebra may be realized as subquotients of such modules of Pseudodifferential Operators. This gives easy proofs of the existence of many previously known uniserial modules, and moreover yields some hitherto undiscovered.
U J Wiese - One of the best experts on this subject based on the ideXlab platform.
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asymptotic freedom dimensional transmutation and an infrared conformal fixed point for the δ function potential in one dimensional relativistic quantum mechanics
Physical Review D, 2014Co-Authors: M H Alhashimi, Abouzeid M Shalaby, U J WieseAbstract:We consider the Schrodinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the Pseudodifferential Operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.
O. V. Fedukh - One of the best experts on this subject based on the ideXlab platform.
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Nonlocal time-multipoint problem for a certain class of evolutionary Pseudodifferential equations with variable symbols: II
Differential Equations, 2017Co-Authors: V. V. Gorodetskii, O. V. Martynyuk, O. V. FedukhAbstract:The properties of the fundamental solution to a nonlocal time-multipoint problem for an evolutionary equation with a Pseudodifferential Operator constructed by a variable symbol are studied. The solvability of the above problem in the class of continuous bounded on R functions is established and a representation of the solution is derived.
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Nonlocal time-multipoint problem for a certain class of evolutionary Pseudodifferential equations with variable symbols: I
Differential Equations, 2017Co-Authors: V. V. Gorodetskii, O. V. Martynyuk, O. V. FedukhAbstract:It has been proved that in generalized spaces of the type S, a Pseudodifferential Operator constructed based on a variable symbol can be treated as the Operator of infiniteorder differentiation if the Operator symbol satisfies certain conditions. The properties of the fundamental solution to a nonlocal time-multipoint problem for the evolutionary equation with this Operator have been studied.
V. V. Gorodetskii - One of the best experts on this subject based on the ideXlab platform.
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Nonlocal time-multipoint problem for a certain class of evolutionary Pseudodifferential equations with variable symbols: II
Differential Equations, 2017Co-Authors: V. V. Gorodetskii, O. V. Martynyuk, O. V. FedukhAbstract:The properties of the fundamental solution to a nonlocal time-multipoint problem for an evolutionary equation with a Pseudodifferential Operator constructed by a variable symbol are studied. The solvability of the above problem in the class of continuous bounded on R functions is established and a representation of the solution is derived.
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Nonlocal time-multipoint problem for a certain class of evolutionary Pseudodifferential equations with variable symbols: I
Differential Equations, 2017Co-Authors: V. V. Gorodetskii, O. V. Martynyuk, O. V. FedukhAbstract:It has been proved that in generalized spaces of the type S, a Pseudodifferential Operator constructed based on a variable symbol can be treated as the Operator of infiniteorder differentiation if the Operator symbol satisfies certain conditions. The properties of the fundamental solution to a nonlocal time-multipoint problem for the evolutionary equation with this Operator have been studied.
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method of hybrid integral transforms for analyzing direct and inverse problems for a class of equations with a Pseudodifferential Operator
Differential Equations, 2013Co-Authors: V. V. Gorodetskii, Ya M DrinAbstract:We use the method of hybrid integral transforms to study the solvability of the direct and inverse problems for a class of equations with a Pseudodifferential Operator constructed from a symbol nonsmooth at zero.
