Browsing Mathematics by Subject "math.FA"
Now showing items 1-17 of 17
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Approximations in $L^1$ with convergent Fourier series
(Springer (part of Springer Nature), 2020)For a separable finite diffuse measure space $\mathcal{M}$ and an orthonormal basis $\{\varphi_n\}$ of $L^2(\mathcal{M})$ consisting of bounded functions $\varphi_n\in L^\infty(\mathcal{M})$, we find a measurable subset ... -
A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
(2021)In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness ... -
Critical Gagliardo-Nirenberg, Trudinger, Brezis-Gallouet-Wainger inequalities on graded groups and ground states
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes the cases of $\mathbb R^n$, ... -
Difference equations and pseudo-differential operators on $\mathbb{Z}^n$
In this paper we develop the calculus of pseudo-differential operators on the lattice $\mathbb{Z}^n$, which we can call pseudo-difference operators. An interesting feature of this calculus is that the phase space is compact ... -
Eigenfunction expansions of ultradifferentiable functions and ultradistributions. III. Hilbert spaces and Universality
(Springer, 2021-03)In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these ... -
Factorizations and Hardy-Rellich inequalities on stratified groups
In this paper, we obtain Hardy, Hardy-Rellich and refined Hardy inequalities on general stratified groups and weighted Hardy inequalities on general homogeneous groups using the factorization method of differential operators, ... -
Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups
(Springer (part of Springer Nature), 2021)We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the H\"ormander-Mihlin-Marcinkiewicz condition. In our analysis, we use ... -
Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary
(2021-01-07)Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the ... -
Hardy inequalities on metric measure spaces, II: The case $p>q$
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on ... -
Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature
(Elsevier, 2021-10)In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of ... -
Harmonic and Anharmonic Oscillators on the Heisenberg Group
(Elsevier, 2021-05-25)Although there is no canonical version of the harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ so far, we make a strong case for a particular choice of operator by using the representation theory of the Dynin-Folland ... -
$L^p$-$L^q$ boundedness of $(k, a)$-Fourier multipliers with applications to Nonlinear equations
(Oxford University Press, 2021)The $(k,a)$-generalised Fourier transform is the unitary operator defined using the $a$-deformed Dunkl harmonic oscillator. The main aim of this paper is to prove $L^p$-$L^q$ boundedness of $(k, a)$-generalised Fourier ... -
$L^p$-bounds for pseudo-differential operators on graded Lie groups
In this work we obtain sharp $L^p$-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the ... -
On a class of anharmonic oscillators
(Elsevier, 2021)In this work we study a class of anharmonic oscillators within the framework of the Weyl-H\"ormander calculus. The anharmonic oscillators arise from several applications in mathematical physics as natural extensions of the ... -
Schatten-von Neumann classes of integral operators
(Elsevier, 2021)In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting ... -
Subelliptic Gevrey spaces
(Wiley, 2020)In this paper, we define and study Gevrey spaces associated with a H\"ormander family of (globally defined) vector fields and its corresponding sub-Laplacian. We show some natural relations between the various Gevrey spaces ... -
Van der Corput lemmas for Mittag-Leffler functions. II. $α$-directions
(Elsevier, 2021-06)The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study ...