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Victoria Nourse - One of the best experts on this subject based on the ideXlab platform.

  • A Tale of Two Lochners : The Untold History of Substantive Due Process and the Idea of Fundamental Rights
    Social Science Research Network, 2009
    Co-Authors: Victoria Nourse
    Abstract:

    To say that the Supreme Court's decision in Lochner v. New York is infamous is an understatement. Scholars remember Lochner for its strong right to contract and laissez-faire ideals -- at least that is the conventional account of the case. Whether one concludes that Lochner leads to the judicial activism of Roe v. Wade, or foreshadows strong property rights, the standard account depends upon an important assumption: that the Lochner era's conception of fundamental rights parallels that of today. From that assumption, it appears to follow that Lochner symbolizes the grave political dangers of substantive due process, with its "repulsive connotation of value-laden" judicial review.This article's thesis is that the conventional account is based on presentist notions of right imposed upon the past. Today, fundamental rights invoked under the Due Process Clause are presumed "fatal in fact," but in 1905 when Lochner was decided, rights claims were common but rarely fatal. Today, fundamental rights trump the general welfare, whereas in 1905, under the police power of the state, the general welfare trumped rights. Today, courts define unenumerated rights in positive terms; they struggle to define the "right to die" or the "right to reject life-saving" treatment. Then, courts assumed rights existed prior to any written constitution, and enumeration was no grand ideal -- rights were defined negatively by drawing limits on federal and state power. As the Fourteenth Amendment itself proclaimed, liberty and property could be deprived subject to "due process," which meant rights were subject to a limit defined by the courts as the "police power." In this sense, the fundamental rights jurisprudence of the Lochner period was the mirror image of today's notion of right-as-trump. Today, no constitutionalist would mistake rational basis for strict scrutiny, but this is precisely what we do when we assume that Lochner-era courts adopted a strong, trumping view of fundamental rights.

  • a tale of two lochners the untold history of substantive due process and the idea of fundamental rights
    California Law Review, 2009
    Co-Authors: Victoria Nourse
    Abstract:

    To say that the Supreme Court’s decision in Lochner v. New York is infamous is an understatement. Scholars remember Lochner for its strong right to contract and laissez-faire ideals—at least that is the conventional account of the case. Whether one concludes that Lochner leads to the judicial activism of Roe v. Wade, or foreshadows strong property rights, the standard account depends upon an important assumption: that the Lochner era’s conception of fundamental rights parallels that of today. From that assumption, it appears to follow that Lochner symbolizes the grave political dangers of substantive due

George A Anastassiou - One of the best experts on this subject based on the ideXlab platform.

Yuri A Kordyukov - One of the best experts on this subject based on the ideXlab platform.

  • Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells
    Mathematische Zeitschrift, 2020
    Co-Authors: Yuri A Kordyukov
    Abstract:

    We consider Toeplitz operators associated with the renormalized Bochner Laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold. We study the asymptotic behavior, in the semiclassical limit, of low-lying eigenvalues and the corresponding eigensections of a self-adjoint Toeplitz operator under assumption that its principal symbol has a non-degenerate minimum with discrete wells. As an application, we prove upper bounds for low-lying eigenvalues of the Bochner Laplacian in the semiclassical limit.

  • the spectral density function of the renormalized Bochner laplacian on a symplectic manifold
    arXiv: Differential Geometry, 2019
    Co-Authors: Yuri A Kordyukov
    Abstract:

    We consider the renormalized Bochner Laplacian acting on tensor powers of a positive line bundle on a compact symplectic manifold. As shown by Guillemin and Uribe, for high tensor powers $p$, its spectrum splits into two parts. One part consists of the eigenvalues which are uniformly bounded independent of $p$, and another part goes to the right at approximately linear rate in $p$. The spectral density function describes the distribution of the uniformly bounded eigenvalues. In this paper, we derive an explicit local formula for the spectral density function in terms of the coefficients of the Riemannian metric and the symplectic form. Our computation heavily relies on methods and results developed by Ma and Marinescu. First, we use the fact that the spectral density function coincides with the leading coefficient in the asymptotic expansion of the generalized Bergman kernel associated with the renormalized Bochner Laplacian. Ma and Marinescu developed a method to compute the coefficients in the asymptotic expansion of the generalized Bergman kernel by recurrence. Using this method, they obtained an integral formula for the first two coefficients and computed explicitly some of them in the almost Kahler case. In the current paper, we start with the Ma-Marinescu formula and complete the computation of the leading coefficient in the general case. As an application, we obtain some additional information on the asymptotic formula for the low-lying eigenvalues of the Bochner Laplacian with discrete wells.

  • generalized bergman kernels on symplectic manifolds of bounded geometry
    Communications in Partial Differential Equations, 2019
    Co-Authors: Yuri A Kordyukov, George Marinescu
    Abstract:

    We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry...

  • semiclassical spectral analysis of toeplitz operators on symplectic manifolds the case of discrete wells
    arXiv: Differential Geometry, 2018
    Co-Authors: Yuri A Kordyukov
    Abstract:

    We consider Toeplitz operators associated with the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold. We study the asymptotic behavior, in the semiclassical limit, of low-lying eigenvalues and the corresponding eigenfunctions of a self-adjoint Toeplitz operator under assumption that its principal symbol has a non-degenerate minimum with discrete wells. As an application, we prove upper bounds for low-lying eigenvalues of the Bochner-Laplacian in the semiclassical limit.

  • generalized bergman kernels on symplectic manifolds of bounded geometry
    arXiv: Differential Geometry, 2018
    Co-Authors: Yuri A Kordyukov, George Marinescu
    Abstract:

    We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtain the relation between the generalized Bergman kernel on a Galois covering of a compact symplectic manifold and the generalized Bergman kernel on the base. Then we state the full off-diagonal asymptotic expansion of the generalized Bergman kernel, improving the remainder estimate known in the compact case to an exponential decay. Finally, we establish the theory of Berezin-Toeplitz quantization on symplectic orbifolds associated with the renormalized Bochner-Laplacian.

Wu Shukun - One of the best experts on this subject based on the ideXlab platform.

Lai Xudong - One of the best experts on this subject based on the ideXlab platform.

  • Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori
    'Springer Science and Business Media LLC', 2021
    Co-Authors: Lai Xudong
    Abstract:

    In this paper, we establish the full $L_p$ boundedness of noncommutative Bochner-Riesz means on two-dimensional quantum tori, which completely resolves an open problem raised in \cite{CXY13} in the sense of the $L_p$ convergence for two dimensions. The main ingredients are sharp estimates of noncommutative Kakeya maximal functions and geometric estimates in the plane. We make the most of noncommutative theories of maximal/square functions, together with microlocal decompositions in both proofs of sharper estimates of Kakeya maximal functions and Bochner-Riesz means.Comment: 37 pages, 2 figures, to appear in Comm. Math. Phy

  • Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori
    2021
    Co-Authors: Lai Xudong
    Abstract:

    In this paper, we establish the full $L_p$ boundedness of noncommutative Bochner-Riesz means on two-dimensional quantum tori, which completely resolves an open problem raised in \cite{CXY13} in the sense of the $L_p$ convergence for two dimensions. The main ingredients are sharper estimates of noncommutative Kakeya maximal functions and geometric estimates in the plain. We make the most of noncommutative theories of maximal/square functions, together with microlocal decompositions in both proofs of sharper estimates of Kakeya maximal functions and Bochner-Riesz means. We point out that even geometric estimates in the plain are different from that in the commutative case.Comment: 41 pages, 2 figure

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