Partial Inner Product Spaces

• General Theory: Algebraic Point of View.- General Theory: Topological Aspects.- Operators on PIP-Spaces and Indexed PIP-Spaces.- Examples of Indexed PIP-Spaces.- Refinements of PIP-Spaces.- Partial #x002A;-Algebras of Operators in a PIP-Space.- Applications in Mathematical Physics.- PIP-Spaces and Signal Processing.

From the reviews: "Partial Inner Product (PIP) spaces generalize and synthesize a lot of spaces appearing in functional analysis, such as rigged Hilbert spaces, scales of Hilbert or Banach spaces, etc. ... the book will be of interest for researchers interested in function spaces as well as for those interested in applications in theoretical physics and signal processing." (Stefan Cobzas, Zentralblatt MATH, Vol. 1195, 2010) "The topic of this book is so-called PIP (partial inner product) spaces, which are vector spaces with a symmetric relation on pairs of elements ... . Overall the book provides a unique opportunity for researchers working in the field of analysis to take a new perspective on more or less well known families of function spaces or operators, and the common functional analytic features common to all these families, analyzed in a very systematic way. ... many readers will enjoy studying the proposed concepts." (Hans G. Feichtinger, Mathematical Reviews, Issue 2011 i)