Gelfand

Gelfand is a surname of Jewish-Russian origin that appears in the names of several prominent mathematicians and in various mathematical constructions. The most influential bearer is Israel Moiseevich Gel′fand (1913–2009), a Soviet mathematician whose work spanned functional analysis, representation theory, and mathematical physics. Gel′fand’s research helped shape many areas of modern analysis and operator theory, and his ideas fostered a wide range of techniques used throughout mathematics.

Numerous concepts and theorems carry the Gelfand name. The Gelfand representation (Gel′fand transform) associates to a commutative C*-algebra a space of continuous functions on its spectrum, linking algebraic and topological structures. The Gelfand–Naimark theorem provides a global characterization of C*-algebras as norm-closed *-subalgebras of bounded operators on a Hilbert space, with the commutative case yielding a spectral representation. The GNS (Gelfand–Naimark–Segal) construction realizes states as representations of C*-algebras. In representation theory, the Gelfand–Tsetlin pattern (basis) offers a combinatorial tool for constructing representations of unitary and general linear groups. The concept of a Gelfand pair arises in harmonic analysis on groups, describing a situation in which certain bi-invariant function spaces are commutative. The rigged Hilbert space, or Gelfand triple, provides a framework for including generalized eigenvectors in quantum mechanics.

Beyond Israel Gel′fand, the surname appears in various contexts within mathematics and the physical sciences, reflecting a broad influence on 20th-century theory. The name is commonly encountered in mathematical literature and is associated with foundational ideas in analysis, algebra, and quantum theory.