Convolutional Calculus

Inhaltsverzeichnis

• 1. Convolutions of Linear Operators. Multipliers and Multiplier Quotients.
• 1.1. The Duhamel Convolution.
• 1.2. The Mikusi? ski Ring.
• 1.3. Convolutions of Linear Endomorphisms.
• 1.4. The Multiplier Quotients Ring of an Annihilators-free Convolutional Algebra.
• 2. Convolutions of General Integration Operators. Applications.
• 2.1. Convolutions of the Linear Right Inverses of the Differentiation Operator.
• 2.2. An Application of the Convolutional Approach to Dirichlet Expansions of Locally Holomorphic Functions.
• 2.3. A Convolution for the General Right Inverse of the Backward Shift Operator in Spaces of Locally Holomorphic Functions.
• 2.4. Convolutions and Commutants of the Gelfond-Leontiev Integration Operator and of Its Integer Powers.
• 2.5. Operational Calculi for the Bernoulli Integration Operator.
• 3. Convolutions Connected with Second-Order Linear Differential Operators.
• 3.1. Convolutions of Right Inverse Operators of the Square of the Differentiation.
• 3.2. Convolutions of Initial Value Right Inverses of Linear Second-Order Differential Operators.
• 3.3. Convolutions of Boundary Value Right Inverses of Linear Second-Order Differential Operators.
• 3.4. Applications of Convolutions to Non-Local Boundary Value Problems.
• References.
• Authors index.