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The left adjoint of derived parabolic induction
We prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod p representations of a p -adic...
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Adjoint Functors
This chapter deals with one of the most important notions in category theory: adjoint functors. Several descriptions of adjoint functors are...
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Universal Envelo** Algebras of Lie–Rinehart Algebras as a Left Adjoint Functor
We prove how the universal envelo** algebra constructions for Lie–Rinehart algebras and anchored Lie algebras are naturally left adjoint functors....
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Geometric Methods for Adjoint Systems
Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or...
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A primer on eigenvalue problems of non-self-adjoint operators
Non-self adjoint operators describe problems in science and engineering that lack symmetry and unitarity. They have applications in...
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Product Approximations of Self-Adjoint Semigroups
In this chapter, we proceed with a systematic analysis of the main for this book subject: the product formulæ approximations in the operator-norm...
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The adjoint of an operator on a Banach space
Self-adjoint operators in smooth Banach spaces have been already defined in recent works. Here, we extend the concept of adjoint of an operator to...
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Transmutations for Self-Adjoint Differential Operators
AbstractMade equations for the kernel of the transformation operator in self-adjoin differential operators. The main factor that makes it possible to...
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On creating new essential spectrum by self-adjoint extension of gapped operators
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily...
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Construction of Jacobi forms using adjoint of the Jacobi–Serre derivative
In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi...
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Discrete Adjoint Computations for Relaxation Runge–Kutta Methods
Relaxation Runge–Kutta methods reproduce a fully discrete dissipation (or conservation) of entropy for entropy stable semi-discretizations of...
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Aerodynamic shape optimization of wind turbine rotor blades using the continuous adjoint method
This paper presents the development of the continuous adjoint method for incompressible fluid flows, solved for the absolute velocity in the relative...
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Chambolle–Pock’s Primal-Dual Method with Mismatched Adjoint
The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point...
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Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces
This article is a revised version of the lectures given by the author at KROMSH-2019. These lectures are devoted to describing a few different ways...
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Generic Stability for Self-Adjoint Semigroups
Category theorems for self-adjoint semigroups are presented; for some classes of self-adjoint semigroups, it is shown that, typically in Baire’s...
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Classical Self-Adjoint Extension Schemes
This chapter presents the two classical self-adjoint extension theories a la von Neumann and a la Kreı̆n, Višik, and Birman. We start with the...
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A novel discrete adjoint-based level set topology optimization method in B-spline space
This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint...
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The Katzarkov–Kontsevich–Pantev conjecture for minimal adjoint orbits
We consider minimal semisimple adjoint orbits as Landau–Ginzburg models and prove that they satisfy the conjecture of Katzarkov–Kontsevich–Pantev...
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Skew-Adjoint Maps and Quadratic Lie Algebras
The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized
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