Extended Abstracts 2021/2022: Ghent Analysis and PDE Seminar (Trends in Mathematics, 2)

Preface
Contents
Part I Analysis
	1 A Note on a Capelli Operator and its Resonance
		1.1 Introduction
		1.2 The Group Actions
		1.3 Two Useful Decompositions
		1.4 Resonances
		1.5 Further remarks
		References
	2 Schatten-von Neumann Classes  on the Torus for
		2.1 Introduction
		2.2 Schatten Classes on the Torus for Small Exponents
		2.3 State-of-the-Art
		References
	3 Log-Sobolev and Nash Inequalities on Graded Groups
		3.1 Introduction
		3.2 Preliminary Notions on Graded Lie Groups
		3.3 Auxiliary and Main Results
			3.3.1 Auxiliary Results
			3.3.2 Main Results
		References
	4 One-Sided Hardy-Littlewood Maximal Functionon Generalised Lorentz Spaces
		4.1 Introduction and Preliminaries
		4.2 Main Results
			4.2.1 Characterisation of Weights and Concluding Remarks
		References
	5 Remarks on Gradient Yamabe Solitons
		5.1 Introduction
		5.2 Gradient Yamabe Warped Product
		5.3 Applications
		References
	6 Boundedness of Fourier Multipliers on Fundamental Domains of Lattices
		6.1 Introduction
		6.2 Main Results
		6.3 Research Perspectives
		References
	7 Pointwise Domination and Weak  Boundednessof Littlewood-Paley Operators via Sparse Operators
		7.1 Introduction
		References
	8  Boundedness of Fourier Multipliers on Graded Lie Groups
		8.1 Introduction
		8.2 Weak (1,1) and Lp Boundedness of Tσ
		8.3 Hp(G) →Lp(G) Boundedness of Tσ
		References
	9 On a Reverse Integral Hardy Inequality on Polarisable Metric Measure Space
		9.1 Introduction
		9.2 Main Results
		9.3 Applications
		References
	10 Logarithmic Sobolev Inequalities of Fractional Orderon Noncommutative Tori
		10.1 Introduction
		10.2 Preliminaries
			10.2.1 Noncommutative Tori
			10.2.2 Sobolev and Lp-Spaces
			10.2.3 Jensen\'s Operator Inequality
		10.3 The Proof of Theorem 10.1
		References
	11 The Prabhakar Fractional -Integral and -DifferentialOperators
		11.1 Introduction
		11.2 Preliminaries
		11.3  The Definitions and the Main Properties of the Prabhakar Fractional q-Integral and q-Differential Operators
		11.4 A Cauchy Type Problem Associated with q-Prabhakar Differential Operator
		References
	12 A Note on Boundedness Properties of Pseudo-Differential Operators on Rank One Symmetric Spaces of Noncompact Type
		12.1 Introduction
		12.2 Preliminaries
			12.2.1 Fourier Transform
		12.3 Results on Boundedness of Pseudo-Differential Operators on X
		References
	13 - Norms of Spectral Multipliers
		13.1 Introduction
		13.2 Weighted Subcoercive Operators and Spectral Estimates
			13.2.1 Weighted Lie Algebras and Their Contractions
			13.2.2 Differential Operators
		References
	14 Estimates for Oscillatory Integrals with DiscontinuousAmplitude
		14.1 Introduction
		14.2 A Model Case
		14.3 A More General Case
		14.4 Sharpness of Result
		References
	15 The Unitary Dual of the Heisenberg Group Over
		15.1 The Ring Rp
		15.2 The Heisenberg Group Over Rp
		15.3 Applications
		References
	16 Critical Sobolev-Type Identities and Inequalitieson Stratified Lie Groups
		16.1 Introduction
		16.2 Critical Sobolev-Type Identity and Inequality on
		16.3 Critical Sobolev-Type Identity on Stratified Lie Groups
		References
Part II Partial Differential Equations
	17 Anisotropic Picone Type Identities for General Vector Fields and Some Applications
		17.1 Introduction and Preliminaries
			17.1.1 Introduction
			17.1.2 Anisotropic Sub-Laplacian for General Vector Fields
		17.2 Anisotropic Picone Identities for Subelliptic p-Laplacian
		17.3 Some Applications
			17.3.1 Functional Setting
			17.3.2 Nonlinear Anisotropic p-Sub-Laplacian Equation
			17.3.3 Applications
				17.3.3.1 Anisotropic Sturmian Comparison Principle
				17.3.3.2 Liouville Type Principle
				17.3.3.3 Anisotropic Quasilinear System with Singular Nonlinearities
				17.3.3.4 Weighted Anisotropic Hardy Inequalities
		References
	18 An Equivalence Between the Neumann Problemand Its Boundary Domain Integral Equation Systemsfor Stokes Equations
		18.1 Introduction
		18.2 Formulation of the Boundary Value Problem
		18.3 Parametrix and Parametrix-Based Hydrodynamic Potentials
			18.3.1 Parametrix and Remainder
			18.3.2 Volume and Surface Potentials
		18.4 The Third Green Identities
		18.5 BDIE Systems for Neumann BVP
			18.5.1 BDIE System (N1)
			18.5.2 BDIE System (N2)
		18.6 Equivalence and Invertibility Theorems
		References
	19 Short Note on Generalised Bivariate Mittag-Leffler-TypeFunctions
		19.1 Introduction
		19.2 Definitions of Some Functions of the Mittag-Leffler-Type
		19.3 Determining the Region of the Convergence of a Function D1
		19.4 Integral Representations of a Function D1
		19.5 Integral Laplace Transforms
		19.6 System of Partial Differential Equations
		References
	20 Inverse Problems for Time-Fractional Mixed Equation Involving the Caputo Fractional Derivative
		20.1 Introduction and Formulation of a Problem
		20.2 Short Description of the Investigation
		References
	21 Time Dependent Inverse Source Problemsfor Integrodifferential Kelvin-Voigt System
		21.1 Introduction
			21.1.1 Statement of the Problem
		21.2 Preliminaries: An Equivalent Nonlocal Direct Problem
		21.3 Existence of a Weak Solution to Inverse Problem (21.1)–(21.5)
		21.4 Existence and Uniqueness of Strong Solution to (21.14) and (21.3)–(21.4)
		21.5 Some Special Cases of (21.1)–(21.5) Removing Restriction (21.15)
		References
	22 A Nonlocal Initial Conditional Boundary Value Problemon Metric Graph
		22.1 Introduction
		22.2 Preliminaries
			22.2.1 Fractional Derivatives and Integrals
			22.2.2 Metric Graphs
		22.3 Problem Formulation
		22.4 Uniqueness of Solution
		22.5 Existence of Solution
		References
	23 Second-Order Semiregular Non-Commutative Harmonic Oscillators: The Spectral Zeta Function
		23.1 Introduction
		23.2 Excursus of Previous Results
		23.3  Non-Commutative Harmonic Oscillators (NCHOs)
		23.4 Parabolic Calculus
		23.5 Parametrix of the Heat-Semigroup
		23.6 Vanishing Property
		23.7 Meromorphic Continuation of ζAw
		References
	24 Global Well-Posedness with Loss of Regularity for a Class of Singular Hyperbolic Cauchy Problems
		24.1 Introduction
		24.2 Our Philosophy of Conjugation
		24.3 Subdivision of the Extended Phase Space
		24.4 Results
		24.5 Cone Condition
		References
	25 On a Mixed Equation Involving Prabhakar Fractional Order Integral-Differential Operators
		25.1 Auxiliary Part: Cauchy Problem
		25.2 Direct and Inverse Problems
		References
	26 Inverse Problem of Determining a Time-Dependent Source in a Fractional Langevin-Type Partial Differential Equation
		26.1 Introduction
			26.1.1 Mathematical Setting
		26.2 Main Results
			26.2.1 Uniqueness of the Solution
			26.2.2 Existence Result
		References
	27 Very Weak Solution of the Discrete Wave Equation for Harmonic Oscillator
		27.1 Introduction
		27.2 Preliminaries
		27.3 Main Results
		References
	28 An Estimate for the Multivariate Mittag-Leffler Function
		28.1 Introduction
		28.2 Main Result
		28.3 Example
		References
Part III Mathematical Modelling
	29 Mathematical Modelling of the Lomb–Scargle Method in Astrophysics
		29.1 Introduction
		29.2 Application in Astrophysics
		29.3 Conclusion
		References
	30 The Application of Physics Informed Networks to Solve Hyperbolic Partial Differential Equations with Nonconvex Flux Function and Diffusion Term
		30.1 Introduction
		30.2 Multi-Phase Transport Problem
		30.3 Physics-Informed Neural Networks
		30.4 Result
		30.5 Conclusion
		References
	31 Fractional Differential Equations: A Primer for Structural Dynamics Applications
		31.1 Introduction
		31.2 Material Response
		31.3 Equation of Motion
		31.4 Frequency Response Function
		31.5 Superposition Principle
		31.6 State-Space Approach
		31.7 Nonlinear Fractional Structural Dynamics
		31.8 Concluding Remarks
		References
	32 Text Matching as Time Series Matching
		32.1 Introduction
		32.2 Proposed Method
			32.2.1 The Recall Stage
			32.2.2 The Ranking Stage
		32.3 Experiments
			32.3.1 Datasets
			32.3.2 The Priori Experiments
			32.3.3 Main Experiments
				32.3.3.1 BM25
				32.3.3.2 RAM-CNN
				32.3.3.3 The Two-Stage Matching Model
		32.4 Conclusion
		References
	33 Performing Particle Image Segmentation on an Extremely Small Dataset
		33.1 Introduction
		33.2 Proposed Method
			33.2.1 KNN Matting
			33.2.2 Data Augmentation
			33.2.3 Network Architecture
		33.3 Experiments
		33.4 Conclusion
		References
	34 Two-Dimensional Dispersed Composites on a Square Torus
		34.1 Introduction
		34.2 Main Results
		34.3 Conclusion
		References