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Continuity and compactness properties of pseudo-differential operators

, 2007
Buzano, Ernesto, Toft, Joachim,
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Differential Operators

Principles of Applied Mathematics, 2019
James P. Keener
semanticscholar   +3 more sources

Spectral Theory and Differential Operators

Oxford Scholarship Online, 2018
This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and makes applications to such questions.
D. Edmunds, D. Evans
semanticscholar   +1 more source

Monogenic Differential Operators

Results in Mathematics, 1992
It is well-known that a homogeneous polynomial of degree \(k\) admits a harmonic Fischer decomposition. But when dealing with Clifford algebra- valued functions, this decomposition can be refined, since every spherical harmonic can be written as the sum of a so-called inner and an outer spherical monogenic.
Sommen, F., Van Acker, N.
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Associative Differential Operations

The Annals of Mathematics, 1950
Die Bezeichnungen \(D\)-Körper, D. P., und die Symbole \(y_i = y_{i0}\), \(y_{ir}\) usw. haben dieselbe Bedeutung. wie in der unmittelbar vorangehenden Besprechung Zbl 0037.18402. Gebildet werden formale \glqq Potenzreihen\grqq{} \(\mathfrak A(y) = A^{(1)}(y) + A^{(2)}(y) + \cdots\), bei denen jeweils \(A^{(i)}(y)\) ein D. P.
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Neural Operators with Localized Integral and Differential Kernels

International Conference on Machine Learning
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications.
Miguel Liu-Schiaffini, Julius Berner, B. Bonev, Thorsten Kurth, K. Azizzadenesheli, Anima Anandkumar   +5 more
semanticscholar   +1 more source

Pseudo‐differential operators

Communications on Pure and Applied Mathematics, 1965
Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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Homogenization of Differential Operators

Acta Mathematicae Applicatae Sinica, English Series, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON SECOND ORDER DIFFERENTIAL OPERATORS

The Annals of Mathematics, 1955
Nevertheless, (1.2) is meaningful only under differentiability conditions which are unnatural for (1.1). An adjoint to (1.1) exists always, but it cannot be written in terms of derivatives with respect to x. The characteristic property of A appears to be (1) that it is of local character, (2) that whenever f has a local minimum at xo and f(xo) = 0 ...
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