Linear partial differential operators and generalized distributions
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Publication:2530233
DOI10.1007/BF02590963zbMath0166.36501MaRDI QIDQ2530233
Publication date: 1966
Published in: Arkiv för Matematik (Search for Journal in Brave)
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Beurling ultradistributions of \(L_{p}\)-growth ⋮ On the moment problem in the spaces of ultradifferentiable functions of mean type ⋮ Extension of ultradifferentiable functions ⋮ Solvability of convolution operators ⋮ Convolution equations and spaces of ultradifferential functions ⋮ Characterization of convolution operators on spaces of \(C^{\infty}\)- functions admitting a continuous linear right inverse ⋮ \(\omega\)-hypoelliptic differential operators of constant strength ⋮ Inhomogeneous Gevrey classes and ultradistributions ⋮ Sequence space representations for weighted solution spaces of hypoelliptic systems of partial differential operators ⋮ On subadditivity-like conditions for associated weight functions ⋮ Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions ⋮ Some embedding theorems for Hörmander-Beurling spaces ⋮ Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms ⋮ Optimal embeddings of ultradistributions into differential algebras ⋮ Boehmians and generalized functions ⋮ On Fourier transforms of distribution semigroups ⋮ Convolution equations in Beurling's distributions ⋮ Global hypoellipticity and simultaneous approximability in ultradifferentiable classes ⋮ Ultradifferentiable Chevalley theorems and isotropic functions ⋮ Microlocal quasianalyticity for distributions and ultradistributions. ⋮ Surjective partial differential operators on spaces of ultradifferentiable functions of Roumieu type ⋮ Navier-Stokes equation in super-critical spaces \(E_{p,q}^s\) ⋮ On the solvability of convolution equations in Beurling's distributions ⋮ Time-frequency analysis of Sjöstrand's class ⋮ The theorem of iterates for elliptic and non-elliptic operators ⋮ Ultradifferentiable extension theorems: a survey ⋮ The Borel map in the mixed Beurling setting ⋮ Maximal inequalities, Fourier multipliers, Littlewood-Paley theorems, and approximations by entire analytic functions in weighted spaces ⋮ Fréchet spaces invariant under differential operators ⋮ Holomorphic approximation of ultradifferentiable functions ⋮ The overdetermined Cauchy problem for \(\omega \)-ultradifferentiable functions ⋮ Geometric microlocal analysis in Denjoy-Carleman classes ⋮ Hankel transformation and Hankel convolution of tempered Beurling distributions. ⋮ The Gabor wave front set in spaces of ultradifferentiable functions ⋮ Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting ⋮ Non-quasianalytic curves in Fréchet spaces ⋮ Oscillation of Fourier integrals with a spectral gap. ⋮ The nuclearity of Gelfand-Shilov spaces and kernel theorems ⋮ Structure theorem for functionals in the space \(\mathfrak S^{\prime}_{\omega_1,\omega_{2}}\) ⋮ Denjoy-Carleman classes: boundary values, approximate solutions and applications ⋮ On weighted \(L_p\)-spaces of vector-valued entire analytic functions ⋮ The action of operator semigroups on the topological dual of the Beurling-Björck space ⋮ On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth ⋮ On sequence space representations of Hörmander--Beurling spaces ⋮ The choice of test functions in gauge quantum field theories ⋮ Superposition in classes of ultradifferentiable functions ⋮ The splitting condition for the weighted \(\overline \partial\)-complex ⋮ Periodic tempered distributions of Beurling type and periodic ultradifferentiable functions with arbitrary support ⋮ On some iterated weighted spaces ⋮ Wavelets in a generalized Sobolev space ⋮ Euclidean Green's functions for Jaffe fields ⋮ Cauchy and Poisson integral of the convolutor in Beurling ultradistributions of \(L_p\)-growth ⋮ Spezielle Sobolev-Räume von Beurling-Distributionen ⋮ Der Satz von Bochner-Schwartz für Ultradistributionen ⋮ Konstruktion von Fundamentallösungen für Convolutoren ⋮ Intersection properties of weak analytically uniform classes of functions ⋮ Generic results in classes of ultradifferentiable functions ⋮ Regularity of global solutions of partial differential equations in non isotropic ultradifferentiable spaces via time-frequency methods ⋮ Invariant subspaces in the theory of operators and theory of functions ⋮ Hyperbolic equations, function spaces with exponential weights and Nemytskij operators ⋮ The KPZ equation on the real line ⋮ Approximation of linear canonical wavelet transform on the generalized Sobolev spaces ⋮ The application of DeWitt-Morette path integrals to general relativity ⋮ Real Paley-Wiener theorems in spaces of ultradifferentiable functions ⋮ Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. I ⋮ On the extension of Whitney ultrajets of Beurling type ⋮ Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model ⋮ Multiwavelets in the generalized Sobolev space \(H^{\omega}_W(\mathbb R^n)\) ⋮ Beitrag zum Divisionsproblem für Ultradistributionen und ein Fortsetzungssatz ⋮ Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis ⋮ Multipliers on \(\mathcal{S}_{\omega } (\mathbb{R}^N)\) ⋮ Paley-Wiener-Schwartz type theorem for ultradistributional wavelet transform ⋮ Convolutors on \(\mathcal{S}_{\omega}(\mathbb{R}^N)\) ⋮ On the Laplace transorm of functionals on classes of infinitely differentiable functions ⋮ Spaces of type \(W\), growth of Hermite coefficients, Wigner distribution, and Bargmann transform ⋮ Ultradifferentiable functions and Fourier analysis ⋮ Analytic extension of smooth functions ⋮ Kolmogorov diameters in solution spaces of systems of partial differential equations ⋮ Whitney's extension theorem for ultradifferentiable functions of Beurling type ⋮ Analytic continuation across a linear boundary ⋮ On solvability of convolution equations in spaces of generalized distributions with restricted growth ⋮ Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis ⋮ On certain linear operators in spaces of ultradifferentiable functions ⋮ Almost subadditive weight functions form Braun-Meise-Taylor theory of ultradistributions ⋮ New Paley-Wiener theorems ⋮ Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions ⋮ Towards an explicit construction of local observables in integrable quantum field theories ⋮ Compactness in translation invariant Banach spaces of distributions and compact multipliers ⋮ Banach spaces of distributions having two module structures ⋮ Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions ⋮ Quasi-analyticity for hypoelliptic operators ⋮ On the continuous linear right inverse for convolution operators in spaces of ultradifferentiable functions ⋮ Approximation of ultra-differentiable functions by polynomials and entire functions ⋮ Characterization of local observables in integrable quantum field theories ⋮ Local operators between spaces of ultradifferentiable functions and ultradistributions ⋮ Examples of compact sets with non-empty interior which do not admit a continuous linear extension operator for ultradifferentiable functions of Beurling type ⋮ Weight functions for classes of ultradifferentiable functions ⋮ Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type ⋮ Global wave front sets in ultradifferentiable classes ⋮ Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences
Cites Work
- Harmonic analysis based on certain commutative Banach algebras
- Differential operators of principal type
- On the range of convolution operators
- On the intersection of classes of infinitely differentiable functions
- On the propagation of analyticity of solutions of differential equations with constant coefficients
- Ultra-distributions definies sur \(R^ n\) et sur certaines classes de variétés différentiables
- Sur quelques extensions de la notion de distribution
- Differential equations without solutions
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