Suppose λ is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal functionLλ(x) $$\sum\nolimits_j { \in z} ^{C_j } \exp ( - \lambda (x - j)^2 ),$$ x∈R, satisfying the interpolatory conditionsLk = δ0k,k∈Z. One objective of this paper is to derive several additional properties ofLλ. For example, it is shown thatLλ possesses the signregularity property sgn[Lλ(x)]=sgn[sin(πx)/(πx)],x∈R, and that |Lλ (x)|≤2e8 min {(⌊|x|⌋+1)-1,exp(-λ⌊|x|⌋)},x∈R. The analysis is based on a simple representation formula forLλ and employs some methods from classical function theory. A second consideration in the paper is the Gaussian cardinal-interpolation operatorLλ, defined by the equation (Lλy)(x):= $$\sum\nolimits_{k \in z} {yk^L \lambda } (x - k)$$ ,x∈R, y=(yk)k∈Z. On account of the exponential decay of the cardinal functionLλ,Lλ is a well-defined linear map froml∞ (Z) intoL∞ (R). Its associated operatornorm ‖Lλ‖ is called the Lebesgue constant ofLλ. The latter half of the paper establishes the following estimates for the Lebesgue constant: ‖Lλ‖≍1, λ→∞, and ║Lλ║≍log(1/λ), λ→0+. Suitable multidimensional analogues of these results are also given.