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Article
Besov regularity in non-linear generalized functions
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized funct...
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Article
Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable
We analyse a class of pseudo-differential operators in the Gelfand–Shilov setting whose Weyl symbols are radial in each phase-space variable separately. Namely, the symbols are of the form
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Article
Extension of localisation operators to ultradistributional symbols with super-exponential growth
In the Gelfand–Shilov setting, the localisation operator \(A^{\varphi _1,\varphi _2}_a\) ...
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Article
Modulation spaces associated with tensor products of amalgam spaces
We identify the generalised modulation spaces associated with tensor products of amalgam spaces having a large class of Banach spaces as their local component. As consequences of the main results, we describe ...
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Chapter and Conference Paper
Note on Vector Valued Hardy Spaces Related to Analytic Functions Having Distributional Boundary Values
Analytic functions defined on a tube domain T ...
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Article
Open AccessLocalization of Fréchet Frames and Expansion of Generalized Functions
Matrix-type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the fr...
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Article
Directional Short-Time Fourier Transform of Ultradistributions
We define and analyze the k-directional short-time Fourier transform and its synthesis operator over Gelfand–Shilov spaces $$\mathcal {S}^\alp...
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Article
Open AccessSolutions of Hyperbolic Stochastic PDEs on Bounded and Unbounded Domains
We treat several classes of hyperbolic stochastic partial differential equations in the framework of white noise analysis, combined with Wiener–Itô chaos expansions and Fourier integral operator methods. The i...
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Article
Convolution with the Kernel \(e^{s\langle x\rangle ^q}, q\ge 1, s>0\) Within Ultradistribution Spaces
We consider the existence of convolution of Roumieu type ultradistribution with the kernel \(e^{s(1+|x|^2)^{q/2}}, q\ge 1\) ...
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Article
Infinite order \(\Psi \) DOs: composition with entire functions, new Shubin-Sobolev spaces, and index theorem
We study global regularity and spectral properties of power series of the Weyl quantisation \(a^w\) ...
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Article
Noether’s theorem for variational problems of Herglotz type with real and complex order fractional derivatives
A variational principle of Herglotz type with a Lagrangian that depends on fractional derivatives of both real and complex orders is formulated, and the invariance of this principle under the action of a local...
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Article
Wave Propagation Dynamics in a Fractional Zener Model with Stochastic Excitation
Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the c...
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Article
Defect distributions applied to differential equations with power function type coefficients
We analyze weakly convergent sequences in weighted Sobolev spaces using global pseudo-differential calculus with non-isotropic symbols and we prove the existence of so called defect distributions. Then we appl...
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Article
f-Frequently hypercyclic \(C_{0}\) -semigroups on complex sectors
We analyze f-frequently hypercyclic, q-frequently hypercyclic ( \(q> 1\) q > 1 ), and frequently hypercyclic \(C_{0}\) C 0 -semigroups ( \(q=1\) q = 1 ) defined on complex sectors,with values in sepa...
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Article
A Paley–Wiener theorem in extended Gevrey regularity
In this paper we introduce appropriate associated function to the sequence \(M_p=p^{\tau p^{\sigma }}, p\in {\mathbf {N}}, \tau>0, \sigma >1\)Mp=pτpσ,p∈N,τ>0,σ>1, and derive its sharp asymptotic estimates in term...
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Article
Multiresolution expansions and wavelets in Gelfand–Shilov spaces
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand–Shilov spaces. Important exampl...
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Chapter
Convolution and Anti-Wick Quantisation on Ultradistribution Spaces
We present recent advances in convolution theory for the quasi-analytic and non quasi-analytic ultradistribution spaces and generalised Gelfand-Shilov spaces. Additionally, we consider the existence of convolu...
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Chapter
The Shearlet Transform and Lizorkin Spaces
We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here th...
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Article
Variational problems of Herglotz type with complex order fractional derivatives and less regular Lagrangian
We derive optimality conditions for variational problems of Herglotz type whose Lagrangian depends on fractional derivatives of both real and complex order, and resolve the case of subdomain when the lower bou...
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Article
Directional Time–Frequency Analysis and Directional Regularity
We improve some of the results related to the directional short-time Fourier transform by fixing the direction and extend them to the spaces ...
