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Relevant bibliographies by topics / H-Pseudodifferential operators

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Academic literature on the topic 'H-Pseudodifferential operators'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "H-Pseudodifferential operators"

1

Yang, Jie. "On L 2 -Boundedness of h -Pseudodifferential Operators." Journal of Function Spaces 2021 (February 20, 2021): 1–5. http://dx.doi.org/10.1155/2021/6690963.

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Let T a h be the h -pseudodifferential operators with symbol a . When a ∈ S ρ , 1 m and m = n ρ − 1 / 2 , it is well known that T a h is not always bounded in L 2 ℝ n . In this paper, under the condition a x , ξ ∈ L ∞ S ρ n ρ − 1 / 2 ω , we show that T a h is bounded on L 2 .

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2

Taylor, Michael. "The Technique of Pseudodifferential Operators (H. O. Cordes)." SIAM Review 38, no. 3 (1996): 540–42. http://dx.doi.org/10.1137/1038101.

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3

Deng, Yu-long. "Commutators of Pseudodifferential Operators on Weighted Hardy Spaces." Journal of Mathematics 2022 (January 20, 2022): 1–6. http://dx.doi.org/10.1155/2022/8851959.

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In this paper, we establish an endpoint estimate for the commutator, b , T , of a class of pseudodifferential operators T with symbols in Hörmander class S ρ , δ m R n . In particular, there exists a nontrivial subspace of B M O R n such that, when b belongs to this subspace, the commutators b , T is bounded from H ω 1 R n into L ω 1 R n , which we extend the well-known result of Calderón-Zygmund operators.

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4

Hitrik, Michael, and Johannes Sjöstrand. "Non-Selfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point." Canadian Journal of Mathematics 60, no. 3 (2008): 572–657. http://dx.doi.org/10.4153/cjm-2008-028-3.

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AbstractThis is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2, having a periodic classical flow. Assuming that the strength ॉ of the perturbation is in the range h2 ≪ ॉ ≪ h1/2 (and may sometimes reach even smaller values), we get an asymptotic description of the eigenvalues in rectangles [−1/C, 1/C] + iॉ[F0 − 1/C, F0 + 1/C], C ≫ 1, when ॉF0 is a saddle point value of the flow average of the leading perturbation.

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5

Rabinovich, V. S. "Local exponential estimates for h-pseudodifferential operators and tunneling for Schrödinger, Dirac, and square root Klein-Gordon operators." Russian Journal of Mathematical Physics 16, no. 2 (2009): 300–308. http://dx.doi.org/10.1134/s1061920809020149.

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6

Rabinovich, V. "Exponential estimates of solutions of pseudodifferential equations on the lattice $${(h \mathbb{Z})^{n}}$$ : applications to the lattice Schrödinger and Dirac operators." Journal of Pseudo-Differential Operators and Applications 1, no. 2 (2010): 233–53. http://dx.doi.org/10.1007/s11868-010-0005-2.

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7

Elong, Ouissam. "On the LP boundedness of h-Fourier integral operators with rough symbols." Mathematica Montisnigri 54 (2022): 25–39. http://dx.doi.org/10.20948/mathmontis-2022-54-3.

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We prove LP boundedness of a class of semiclassical Fourier integral operators defined by smooth phase function and semiclassical rough symbols on the spatial variable 𝑥. We also consider a spacial case of ℎ -pseudodifferential operators.

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8

Orlov, A. Yu, and P. Winternitz. "P∞ Algebra of KP, Free Fermions and 2-Cocycle in the Lie Algebra of Pseudodifferential Operators." International Journal of Modern Physics B 11, no. 26n27 (1997): 3159–93. http://dx.doi.org/10.1142/s0217979297001532.

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The symmetry algebra P∞=W∞⊕ H ⊕ I∞ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one ("positive") half of the point symmetries belongs to the W∞ symmetries while the other ("negative") part belongs to the I∞ ones. The corresponding action on the τ-function is obtained. A new embedding of the Virasoro algebra into gl(∞) describes conformal transformations of the KP time variables. A free fermion algebra cocycle is described as a PDO Lie algebra cocycle.

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9

Rozendaal, Jan. "Rough Pseudodifferential Operators on Hardy Spaces for Fourier Integral Operators II." Journal of Fourier Analysis and Applications 28, no. 4 (2022). http://dx.doi.org/10.1007/s00041-022-09959-x.

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AbstractWe obtain improved bounds for pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $$a(x,\eta )$$ a ( x , η ) are elements of $$C^{r}_{*}S^{m}_{1,\delta }$$ C ∗ r S 1 , δ m classes that have limited regularity in the x variable. We show that the associated pseudodifferential operator a(x, D) maps between Sobolev spaces $${\mathcal {H}}^{s,p}_{FIO}({{\mathbb {R}}^{n}})$$ H FIO s , p ( R n ) and $${\mathcal {H}}^{t,p}_{FIO}({{\mathbb {R}}^{n}})$$ H FIO t , p ( R n ) over the Hardy space for Fourier integral operators $${\mathcal {H}}^{p}_{FIO}({{\mathbb {R}}^{n}})$$ H FIO p ( R n ) . Our main result is that for all $$r>0$$ r > 0 , $$m=0$$ m = 0 and $$\delta =1/2$$ δ = 1 / 2 , there exists an interval of p around 2 such that a(x, D) acts boundedly on $${\mathcal {H}}^{p}_{FIO}({{\mathbb {R}}^{n}})$$ H FIO p ( R n ) .

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10

"Partial parabolicity of the boundary-value problem for pseudodifferential equations in a layer." V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, no. 89 (2019). http://dx.doi.org/10.26565//2221-5646-2019-89-03.

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A nonlocal boundary-value problem for evolutional pseudodifferential equations in an infinite layer is considered in this paper. The notion of the partially parabolic boundary-value problem is introduced when a solving function decreases exponentially only by the part of space variables. This concept generalizes the concept of a parabolic boundary value problem, which was previously studied by one of the authors of this paper (A. A. Makarov). Necessary and sufficient conditions for the pseudodifferential operator symbol are obtained in which partially parabolic boundary-value problems exist. It turned out that the real part of the symbol of a pseudodifferential operator should increase unboundedly powerfully in some of the spatial variables. In this case, a specific type of boundary conditions is indicated, which depend on a pseudodifferential equation and are also pseudodifferential operators. It is shown that for solutions of partially parabolic boundary-value problems, smoothness in some of the spatial variables increases. The disturbed (excitated) pseudodifferential equation with a symbol which depends on space and temporal variables is also investigated. It has been found for partially parabolic boundary-value problems what pseudodifferential operators are possible to be disturbed in the way that the input equation of this boundary-value problem would remain correct in Sobolev-Slobodetsky spaces. It is also shown that although the properties of increasing the smoothness of solutions in part of the variables for partially parabolic boundary value problems are similar to the property of solutions of partially hypoelliptic equations introduced by L. H\"{o}rmander, these examples show that the partial parabolic boundary value problem does not follow from partial hipoellipticity; and vice versa - an example of a partially parabolic boundary value problem for a differential equation that is not partially hypoelliptic is given.

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