The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Brice Camus - One of the best experts on this subject based on the ideXlab platform.
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a semi classical Trace Formula at a totally degenerate critical level
arXiv: Analysis of PDEs, 2006Co-Authors: Brice CamusAbstract:We study the semi-classical Trace Formula at a critical energy level for an $h$-pseudo-differential operator on $\mathbb{R}^{n}$ whose principal symbol has a totally degenerate critical point for that energy. This problem is studied for a large time behavior and under the hypothesis that the principal symbol of the operator has a local extremum at the critical point.
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contributions of non extremum critical points to the semi classical Trace Formula
Journal of Functional Analysis, 2004Co-Authors: Brice CamusAbstract:We study the semi-classical Trace Formula at a critical energy level for a h-pseudo-differential operator on Rn whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to the Trace Formula of isolated non-extremum critical points under a condition of “real principal type”. The new contribution to the Trace Formula is valid for all time in a compact subset of R but the result is modest since we have restrictions on the dimension.
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a semi classical Trace Formula at a totally degenerate critical level
Communications in Mathematical Physics, 2004Co-Authors: Brice CamusAbstract:We study the semi-classical Trace Formula at a critical energy level for an h-pseudo-differential operator on Open image in new window n whose principal symbol has a totally degenerate critical point for that energy. This problem is studied for a large time behavior and under the hypothesis that the principal symbol of the operator has a local extremum at the critical point.
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a semi classical Trace Formula at a non degenerate critical level
Journal of Functional Analysis, 2004Co-Authors: Brice CamusAbstract:Abstract We study the semi-classical Trace Formula at a critical energy level for a h -pseudodifferential operator whose principal symbol has a unique non-degenerate critical point for that energy. This leads to the study of Hamiltonian systems near equilibrium and near the non-zero periods of the linearized flow. The contributions of these periods to the Trace Formula are expressed in terms of degenerate oscillatory integrals. The new results obtained are Formulated in terms of the geometry of the energy surface and the classical dynamics on this surface.
James Arthur - One of the best experts on this subject based on the ideXlab platform.
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functoriality and the Trace Formula
Simons Symposium on the Trace Formula, 2016Co-Authors: James ArthurAbstract:We shall summarize two different lectures that were presented on Beyond Endoscopy, the proposal of Langlands to apply the Trace Formula to the principle of functoriality. We also include an elementary description of functoriality, and in the last section, some general reflections on where the study of Beyond Endoscopy might be leading.
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an introduction to the Trace Formula
2005Co-Authors: James ArthurAbstract:Part I. The Unrefined Trace Formula 7 1. The Selberg Trace Formula for compact quotient 7 2. Algebraic groups and adeles 11 3. Simple examples 15 4. Noncompact quotient and parabolic subgroups 20 5. Roots and weights 24 6. Statement and discussion of a theorem 29 7. Eisenstein series 31 8. On the proof of the theorem 37 9. Qualitative behaviour of J (f) 46 10. The coarse geometric expansion 53 11. Weighted orbital integrals 56 12. Cuspidal automorphic data 64 13. A truncation operator 68 14. The coarse spectral expansion 74 15. Weighted characters 81
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a stable Trace Formula iii proof of the main theorems
Annals of Mathematics, 2003Co-Authors: James ArthurAbstract:This paper is the last of three articles designed to stabilize the Trace Formula. Our goal is to stabilize the global Trace Formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases. In the first article [I], we laid out the foundations of the process. We also stated a series of local and global theorems, which together amount to a stabilization of each of the terms in the Trace Formula. In the second paper [II], we established a key reduction in the proof of one of the global theorems. In this paper, we shall complete the proof of the theorems. We shall combine the global reduction of [II] with the expansions that were established in Section 10 of [I]. We refer the reader to the introduction of [I] for a general discussion of the problem of stabilization. The introduction of [II] contains further discussion of the Trace Formula, with emphasis on the "elliptic" coefficients aGll('s). These objects are basic ingredients of the geometric side of the Trace Formula.
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a stable Trace Formula i general expansions
Journal of The Institute of Mathematics of Jussieu, 2002Co-Authors: James ArthurAbstract:This is the first of three articles designed to stabilize the global Trace Formula. The results apply to any group for which the fundamental lemma (and its variants for weighted orbital integrals) is valid. The main purpose of this paper is to establish a series of expansions that are parallel to the expansions in the Trace Formula. We shall also Formulate the local and global theorems required to interpret the terms in these expansions. The proofs of the theorems will be given in the subsequent two articles. The expansions of this paper will then yield both a stable Trace Formula, and a decomposition of the ordinary Trace Formula into a linear combination of stable Trace Formulae. AMS 2000 Mathematics subject classification: Primary 22E55. Secondary 11R39
Erez Lapid - One of the best experts on this subject based on the ideXlab platform.
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on the continuity of the geometric side of the Trace Formula
Acta Mathematica Vietnamica, 2016Co-Authors: Tobias Finis, Erez LapidAbstract:We extend the geometric side of Arthur’s non-invariant Trace Formula for a reductive group G defined over \(\mathbb {Q}\) continuously to a natural space \(\mathcal {C}(G(\mathbb {A})^{1})\) of test functions which are not necessarily compactly supported. The analogous result for the spectral side was obtained in [10]. The geometric side is decomposed according to the following equivalence relation on \(G(\mathbb {Q})\): γ1∼γ2 if γ1 and γ2 are conjugate in \(G(\overline {\mathbb {Q}})\) and their semisimple parts are conjugate in \(G(\mathbb {Q})\). All terms in the resulting decomposition are continuous linear forms on the space \(\mathcal {C}(G(\mathbb {A})^{1})\), and can be approximated (with continuous error terms) by naively truncated integrals.
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on the continuity of the geometric side of the Trace Formula
arXiv: Number Theory, 2015Co-Authors: Tobias Finis, Erez LapidAbstract:We extend the geometric side of Arthur's non-invariant Trace Formula for a reductive group $G$ defined over $\mathbb{Q}$ continuously to a natural space $\mathcal{C}(G(\mathbb{A}^1))$ of test functions which are not necessarily compactly supported. The analogous result for the spectral side was obtained in [MR2811597]. The geometric side is decomposed according to the following equivalence relation on $G(\mathbb{Q})$: $\gamma_1\sim\gamma_2$ if $\gamma_1$ and $\gamma_2$ are conjugate in $G(\bar{\mathbb{Q}})$ and their semisimple parts are conjugate in $G(\mathbb{Q})$. All terms in the resulting decomposition are continuous linear forms on the space $\mathcal{C}(G(\mathbb{A})^1)$, and can be approximated (with continuous error terms) by naively truncated integrals.
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on the spectral side of arthur s Trace Formula absolute convergence
Annals of Mathematics, 2011Co-Authors: Tobias Finis, Erez Lapid, Werner E G MullerAbstract:We derive a renement of the spectral expansion of Arthur’s Trace Formula. The expression is absolutely convergent with respect to the Trace norm.
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on the spectral side of arthur s Trace Formula combinatorial setup
Annals of Mathematics, 2011Co-Authors: Tobias Finis, Erez LapidAbstract:In Arthur’s Trace Formula, a ubiquitous role is played by certain limiting expressions arising from piecewise smooth functions with respect to projections of the Coxeter fan ((G;M)-families). These include terms resulting from intertwining operators on the spectral side and volumes of polytopes on the geometric side. We introduce the combinatorial concept of a compatible family with respect to an arbitrary polyhedral fan and obtain new Formulas for the corresponding limiting expressions in this general framework. Our Formulas can be regarded as algebraic generalizations of certain volume Formulas for convex polytopes. In a companion paper, the results are used to study the spectral side of the Trace Formula.
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on the continuity of arthur s Trace Formula the semisimple terms
Compositio Mathematica, 2011Co-Authors: Tobias Finis, Erez LapidAbstract:We show that the semisimple part of the Trace Formula converges for a wide class of test functions.
Malo Jezequel - One of the best experts on this subject based on the ideXlab platform.
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global Trace Formula for ultra differentiable anosov flows
Communications in Mathematical Physics, 2021Co-Authors: Malo JezequelAbstract:Adapting tools that we introduced in Jezequel (J Spectr Theory 10(1):185–249, 2020) to study Anosov flows, we prove that the Trace Formula conjectured by Dyatlov and Zworski in (Ann. Sci. Ec. Norm. Super. (4) 49(3):543–577, 2016) holds for Anosov flows in a certain class of regularity (smaller than $${\mathcal {C}}^\infty $$ but larger than the class of Gevrey functions). The main ingredient of the proof is the construction of a family of anisotropic Hilbert spaces of generalized distributions on which the generator of the flow has discrete spectrum.
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global Trace Formula for ultra differentiable anosov flows
arXiv: Dynamical Systems, 2019Co-Authors: Malo JezequelAbstract:Adapting tools that we introduced in [19] to study Anosov flows, we prove that the Trace Formula conjectured by Dyatlov and Zworski in [12] holds for Anosov flows in a certain class of regularity (smaller than $\mathcal{C}^\infty$ but larger than the class of Gevrey functions). The main ingredient of the proof is the construction of a family of anisotropic Hilbert spaces of generalized distributions on which the generator of the flow has discrete spectrum.
Tobias Finis - One of the best experts on this subject based on the ideXlab platform.
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on the continuity of the geometric side of the Trace Formula
Acta Mathematica Vietnamica, 2016Co-Authors: Tobias Finis, Erez LapidAbstract:We extend the geometric side of Arthur’s non-invariant Trace Formula for a reductive group G defined over \(\mathbb {Q}\) continuously to a natural space \(\mathcal {C}(G(\mathbb {A})^{1})\) of test functions which are not necessarily compactly supported. The analogous result for the spectral side was obtained in [10]. The geometric side is decomposed according to the following equivalence relation on \(G(\mathbb {Q})\): γ1∼γ2 if γ1 and γ2 are conjugate in \(G(\overline {\mathbb {Q}})\) and their semisimple parts are conjugate in \(G(\mathbb {Q})\). All terms in the resulting decomposition are continuous linear forms on the space \(\mathcal {C}(G(\mathbb {A})^{1})\), and can be approximated (with continuous error terms) by naively truncated integrals.
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on the continuity of the geometric side of the Trace Formula
arXiv: Number Theory, 2015Co-Authors: Tobias Finis, Erez LapidAbstract:We extend the geometric side of Arthur's non-invariant Trace Formula for a reductive group $G$ defined over $\mathbb{Q}$ continuously to a natural space $\mathcal{C}(G(\mathbb{A}^1))$ of test functions which are not necessarily compactly supported. The analogous result for the spectral side was obtained in [MR2811597]. The geometric side is decomposed according to the following equivalence relation on $G(\mathbb{Q})$: $\gamma_1\sim\gamma_2$ if $\gamma_1$ and $\gamma_2$ are conjugate in $G(\bar{\mathbb{Q}})$ and their semisimple parts are conjugate in $G(\mathbb{Q})$. All terms in the resulting decomposition are continuous linear forms on the space $\mathcal{C}(G(\mathbb{A})^1)$, and can be approximated (with continuous error terms) by naively truncated integrals.
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on the spectral side of arthur s Trace Formula absolute convergence
Annals of Mathematics, 2011Co-Authors: Tobias Finis, Erez Lapid, Werner E G MullerAbstract:We derive a renement of the spectral expansion of Arthur’s Trace Formula. The expression is absolutely convergent with respect to the Trace norm.
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on the spectral side of arthur s Trace Formula combinatorial setup
Annals of Mathematics, 2011Co-Authors: Tobias Finis, Erez LapidAbstract:In Arthur’s Trace Formula, a ubiquitous role is played by certain limiting expressions arising from piecewise smooth functions with respect to projections of the Coxeter fan ((G;M)-families). These include terms resulting from intertwining operators on the spectral side and volumes of polytopes on the geometric side. We introduce the combinatorial concept of a compatible family with respect to an arbitrary polyhedral fan and obtain new Formulas for the corresponding limiting expressions in this general framework. Our Formulas can be regarded as algebraic generalizations of certain volume Formulas for convex polytopes. In a companion paper, the results are used to study the spectral side of the Trace Formula.
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on the continuity of arthur s Trace Formula the semisimple terms
Compositio Mathematica, 2011Co-Authors: Tobias Finis, Erez LapidAbstract:We show that the semisimple part of the Trace Formula converges for a wide class of test functions.
